FLUIDS MECHANICS (a letter to a friend) UPDATED+

8.Water at 20°C (ρ=998 kg/m3) flows at 0.00189 m3/s through the 1.9 cm
diameter double pipe bend of the Figure below. The pressures are p1 =
207 kPa and p2 = 165 kPa. Compute the torque T at point B necessary
to keep the pipe from rotating.

Musadoto felician Deus

9.Kerosene at 200 C flows through the pump in Figure at 2.3 ft3/s. Head

losses between 1 and 2 are 8 ft, and the pump delivers 8 hp (1 hp =

550 ft-lbf/s) to the flow. What should the mercury-monometer reading
h ft be? ( ecury=846 b/ 3, erosine=50.2 b/ 3)

Musadoto felician Deus

10. Water at 20°C (ρ=998 kg/m3) flows through the elbow and waterjet
exits to the atmosphere. The waterjet impinges normal to a flat plate
that moves at velocity of 5 m/s as shown in Figure. The pipe diameter
is D1= 10 cm, while D2 = 3 cm. At a flow rate of 0.0153 m3/s, the
pressure p1 = 233 kPa (gage). (a) Estimate x component of the force
on the flange bolts at section 1. (b) Find the force required to keep
plate moving at a constant velocity. Neglect weight of water, elbow
and plate.

Musadoto felician Deus

11. Air ( = 1.31 kg/m3 ) exits from a nozzle, which has the diameter of
7 cm at the section (1) and 4 cm at the section (2), into atmospheric
pressure ( atm = 0 gage). If the manometer fluid has a specific
gravity SG = 0.8 and the manometer reading is = 5 cm, with friction
neglected, determine: (a) The gage pressure at section (1) by using
the manometer reading, (b) Find the relationship between the
velocities at section (1) and (2) using continuity equation, and (c)
Determine the velocity at section (2). (Note: ater = 9,790 N/m3)

Musadoto Bernoulli’s Equation:

felician Deus

12. The belt in the Figure below moves at steady velocity V and skims
the top of a tank of oil of viscosity μ. Neglect air drag. If the
velocity profile is: ( )=1.1547 sin( y/3 )and the belt moves at 2.5
m/s over SAE 30W oil at 20°C (μ = 0.29 kg/m-s) with L = 2 m, b = 60
cm, and h = 3 cm, what is the required belt-drive power P in Watts?

Musadoto felician Deus

13. Air at 20°C and 1 atm (ν=1.5E-5 m2/s) flows at 20 m/s past the flat
plate in the Figure below. A pitot stagnation tube, placed at a
height y from the wall, estimates the local velocity to be u=14.58
m/s at the position of the pitot inlet. (a) If y=2 mm, assume laminar
flow and use the Blasius solution (Table below) to estimate the
downstream position x of the pitot tube and then the boundary layer
thickness δ. (b) If y=10 mm, the flow there cannot possibly be
laminar since for U=20 m/s a laminar boundary layer cannot grow to a
thickness of 10 mm. Therefore assume the flow is turbulent at the
pitot probe and use Prandtl’s approximation to estimate the boundary
layer thickness δ and then the downstream position x of the pitot
tube.

Musadoto felician Deus

14. In the Figure below the connecting pipe is commercial steel (ε=0.046
mm) 6 cm in diameter. Estimate the flow rate, in m3/h, if the fluid
is water at 20°C (ρ=998 kg/m3, μ=0.001 kg/ms).

Musadoto felician Deus

(use moody chart from other problems,Bro! Deus)

15. The horizontal pump in the Figure below discharges water at 57 m3/h.
The losses between 1 and 2 are given by =K 12/2 , where ≈7.5 is a

dimensionless loss coefficient. Take the kinetic energy correction

factor ≈1.06 for both sections 1 and 2 and find the power delivered
to the water by the pump (water density is 1000 kg/m3).

Musadoto felician Deus

16. The water in an aboveground swimming pool is to be emptied by
unplugging a 3-cm-diameter horizontal pipe attached to the bottom of
the pool. Assuming that point 1 at the free surface of the pool and
point 2 at the exit of pipe are open to atmosphere with a vertical
distance of 2m, determine the maximum flow rate of water through the
pipe. Also, explain why the actual flow rate will be less.

Musadoto felician Deus

17. regions far from the entrance, fluid flow through a circular pipe is
one-dimensional and the velocity profile for laminar flow is given by
( )=umax(1-r2/R2)
where is the radius of the pipe, is the radial distance from
the center of the pipe, and ax is the maximum flow velocity, which
occurs at the center. Obtain (a) a relation for the drag force
applied by the fluid on a section of the pipe of length and (b) the
value of the drag force for water flow at 20°C with = 0.08 m, = 15
m, ax = 3 m/s, and = 0.0010 kg/m · s.

Solution felician Deus

Musadoto

18. Water at 20°C is to be pumped from a reservoir (zA = 5 m) to another
reservoir at a higher elevation (zB = 13 m) through two 36-m-long
pipes connected in parallel, as shown in Figure. The pipes are made
of commercial steel, and the diameters of the two pipes are 4 and 8
cm. Water is to be pumped by a 70 percent efficient motor–pump
combination that draws 8 kW of electric power during operation. The
minor losses and the head loss in pipes that connect the parallel
pipes to the two reservoirs are considered to be negligible.
Determine the total flow rate between the reservoirs and the flow
rate through each of the parallel pipes.

(Answer 0.0715 m3/s)
19. The mass flow rate of air at 20°C ( = 1.204 kg/m3) through a 15-cm-

diameter duct is measured with a Venturi meter equipped with a water
manometer. The Venturi neck has a diameter of 6 cm, and the manometer
has a maximum differential height of 40 cm. Taking the discharge
coefficient to be 0.98, determine the maximum mass flow rate of air
this Venturi meter can measure.( Answer: 0.273 kg/s)

Musadoto felician Deus

20. A reducing elbow is used to deflect water flow at a rate of 30 kg/s
in a horizontal pipe upward by an angle of 45° from the flow
direction while accelerating it. The elbow discharges water into the
atmosphere. The crosssectional area of the elbow is 150 cm2 at the
inlet and 25 cm2 at the exit. The elevation difference between the
centers of the exit and the inlet is 40 cm. The mass of the elbow and
the water in it is 50 kg. Determine the anchoring force needed to
hold the elbow in place. Take the momentum-flux correction factor to
be 1.03.

21. A 90° elbow is used to direct water flow at a rate of 25 kg/s in a
horizontal pipe upward. The diameter of the entire elbow is 10 cm.
The elbow discharges water into the atmosphere, and thus the pressure
at the exit is the local atmospheric pressure. The elevation
difference between the centers of the exit and the inlet of the elbow
is 35 cm. The weight of the elbow and the water in it is considered
to be.

22. Water at 15°C flows steadily through the contraction shown in Figure
such that V2 =4V1. If the gage reading is maintained at 120 kPa,
determine the maximum velocity V1 possible before cavitation occurs

Musadoto felician Deus

23. Air at 120 kPa absolute and 30°C flows vertically upward in a pipe,
as shown in Figure. If the water manometer deflection H = 5 cm,
determine the velocity in the smaller pipe. Assume the air to be
incompressible.

24. Air flows from a reservoir at 20°C and 200 kPa absolute through a 5-
cm-diameter throat and exits from a 10-cm-diameter nozzle. Calculate
the exit pressure pe needed to locate a normal shock wave at a
position where the diameter is 7.5 cm.

25. A horizontal pipe 1000 m in length, with a diameter of 500 mm, and a
steady velocity of 0.5 m/s, is suddenly subjected to a new
piezometric head differential of 20 m when the downstream valve
suddenly opens and its coefficient changes to K = 0.2.Assuming a
friction factor of f = 0.02, determine the final steady-state
velocity, and the time when the actual velocity is 75% of the final
value.

26. A rectangular tank 10 m x 5 m and 3.25 m deep is divided by a
partition wall parallel to the shorter wall of the tank. One of the
compartments contains water to a depth of 3.25 m and the other oil of
specific gravity 0.85 to a depth of 2 m.Find the resultant pressure
on the partition.

27. A rectangular plate 1.5m x 3.0m is submerged in water and makes an
angle of 60° with the horizontal, the 1.5m sides being horizontal.
Calculate the magnitude of the force on the plate and the location of
the point of application of the force, with reference to the top edge
of the plate, when the top edge of the plate is 1.2m below the water
surface.

28. Determine the total force and location of centre of pressure for a
circular plate of 2 m dia immersed vertically in water with its top
edge 1.0 m below the water surface.

Musadoto felician Deus

29. A rectangular plate 2 m x 3 m is immersed in oil of specific gravity
0.85 such that its ends are at depths 1.5 m and 3 m respectively.
Determine the total pressure acting on the plate and locate it.

30. A circular plate of dia 0.75 m is immersed in a liquid of relative
density of 0.8 with its plane making an angle of 30 o with the
horizontal. The centre of the plate is at a depth of 1.5 m below the
free surface. Calculate the total force on one side of the plate and
location of centre of pressure.

31. A vertical gate closes a circular tunnel of 5 m diameter running
full of water, the pressure at the bottom of the gate is 0.5
MPa.Determine the hydrostatic force and the position of centre of
pressure.

32. Find the horizontal and vertical component of force and its point of
application due to water per meter length of the gate AB having a
quadrant shape of radius 2 m shown in Fig. Find also the resultant
force in magnitude and direction.

33. A cylinder holds water in a channel as shown in Fig. Determine the
weight of 1 m length of the cylinder.

34. Figure shows the cross section of a tank full of water under
pressure. The length of the tank is 2 m. An empty cylinder lies along
the length of the tank on one of its corner as shown. Find the
resultant force acting on the curved surface of the cylinder.

35. A 500m long pipeline slopes upwards at 1 in 50 and changes from
450mm in diameter to 300mm in diameter 300m from its lower end. If
the frictional head losses in the pipes are 1.0 and 7.0m/km length
respectively and the pressure at the upper end is 120kN/m2, find the
pressure at the lower end when the flow rate in the pipeline is 100
l/s.

Musadoto felician Deus

36. A 45o degree bend is connected in a pipe line, the diameters at the
inlet and outlet of the bend being 600 mm and 300 mm respectively.
Find the force exerted by water on the bend if intensity of pressure
at inlet to bend is 88.29 kPa and rate of flow of water i s 600 lps.

Musadoto felician Deus

37. Water flows up a reducing bend of weight 80kN place in a vertical
plane. For the bend, the inlet diameter is 2 m, outlet diameter is
1.3 m, angle of deflection is 120 o and vertical height (distance
between the inlet and the outlet) is 3 m. If the discharge is 8.5
m3/s, pressure at the inlet is 280 kPa and the head loss is half the
kinetic head at the exit, determine the force on the bend.
HINTS

38. A tapered section in a horizontal pipeline reduces the diameter from
600mm to 50mm in the direction of flow. If the flow rate is 750 l/s
and the upstream pressure is 300 KN/m2, calculate:
(a) The downstream pressure

(b) The magnitude and direction of the force on the taper

Musadoto felician Deus

39. A 450mm diameter pipeline conveying 1.0 m3/s of water contains a

22.5° bend in the horizontal plane. If the pressure in the bend is
250 KN/m2, calculate the magnitude and direction of the force on the

bend.

40. Find the diameter of a Galvanized iron pipe required to carry a flow
of 40lps of water, if the loss of head is not to exceed 5m per 1km.
Length of pipe, Assume f=0.02.( 220mm = D )

41. Two tanks are connected by a 500mm diameter 2500mm long pipe. Find
the rate of flow if thedifference in water levels between the tanks
is 20m. Take f=0.016. Neglect minorlosses.( Q=0.4348m3/secor 434.8lps)

42. Water is supplied to a town of 0.5million inhabitants from a
reservoir 25km away and the loss of head due to friction in the pipe
line is measured as 25m. Calculate the size of the supply main, if
each inhabitant uses 200 litres of water per day and 65% of the daily
supply is pumped in 8 ½ hours. Take f=0.0195.

Musadoto felician Deus

43. An existing pipe line 800m long consists of four sizes namely, 30cm
for 175m, 25cm dia for the next 200m, 20cm dia for the next 250m and
15cm for the remaining length. Neglecting minor losses, find the
diameter of the uniform pipe of 800m. Length to replace the compound
pipe.

44. Two reservoirs are connected by four pipes laid in parallel, their
respective diameters being d, 1.5d, 2.5d and 3.4d respectively. They
are all of same length L & have the same friction factors f. Find the
discharge through the larger pipes, if the smallest one carries
45lps.

Musadoto felician Deus

45. Two pipe lines of same length but with different diameters 50cm and
75cm are made to carry the same quantity of flow at the same
Reynold’s number. What is the ratio of head loss due to friction in
the two pipes?

46. A 30cm diameter main is required for a town water supply. As pipes
over 27.5cm diameter are not readily available, it was decided to lay
two parallel pipes of same diameter. Find the diameter of the
parallel pipes which will have the combined discharge equal to the
single pipe. Adopt same friction factor for all the pipes.
(TRY THIS BRO! DEUS. answer D = 0.205m 0.275m)

Musadoto felician Deus

47. Two reservoirs are connected by two parallel pipes. Their diameter
are 300mm & 350mm and lengths are 3.15km and 3.5km respectively of
the respective values of coefficient of friction are 0.0216 and
0.0325. What will be the discharge from the larger pipe, if the
smaller one carries 285lps? (answer 0.324m3/s)

48. Consider two pipes of same lengths and having same roughness
coefficient, but with the diameter of one pipe being twice the other.
Determine
(a) the ratio of discharges through these pipes, if the head loss
due to friction for both the pipes is the same.(answer 5.656)
(b) (ii) the ratio of the head loss due to friction, when both the
pipes carry the same discharge.(answer 0.03125).

49. Two sharp ended pipes are 50mm & 105mm diameters and 200m length are
connected in parallel between two reservoirs which have a water level
difference of 15m. If the coefficient of friction for each pipes of
0.0215. Calculate the rate of flow in each pipe and also diameter of
a single pipe 200m long which would give the same discharge, if it
were substituted for the Original two pipes.
(answer D=0.1112m=11.12cm)

50. Two pipes with diameters 2D and D are first connected in parallel
and when a discharge Q passes the head loss is H1, when the same
pipes are Connected in series for the same discharge the loss of head
is H2. Find the relationship between H1 and H2. Neglect minor losses.
Both the pipes are of same length and have the same friction factors.

5 MINUTES BREAK BRO Deus

Yes , break is over resume by doing this simple QUIZ bro!.

(a) Explain the concept of Minor Losses in Pipes
Minor losses in a pipe flow can be either due to change in
magnitude or direction of flow.

(b) Why minor losses in pipe
They can be due to one or more of the following reasons.
I. Entry loss
II. Exit loss
III. Sudden expansion loss
IV. Sudden contraction loss
V. Losses due to pipe bends and fittings
VI. Losses due to obstruction in pipe.

Musadoto felician Deus

SUMMARY QUESTIONS BRO! DEUS

1. (a)What is capillarity? Derive an expression for height of a
capillary rise.
(b) What is the difference between cohesion and adhesion?
(c) Determine the minimum size of glass tube that can be used to
measure water level, if the capillary rise in the tube is not to
exceed 0.25 mm. Take surface tension of water in contact with air as
0.0735 N/m.

2.a) Derive an expression for the depth of centre of pressure from free
surface of liquid of an inclined plane surface submerged in the liquid
b) A rectangular sluice gate is situated on the vertical wall of a lock.
The vertical side of the sluice is ‘d’ metres in length and depth of
centroid of the area is ‘p’ metres below thewater surface. derive the
depth of pressure

3.a) Explain Lagrangian and Eulerian methods of describing fluid flow.
b) If the velocity potential function is given by ψ = 3x − 4y. Find the
magnitude and direction of the velocity at any point?

4.a) What is a pitot tube? Explain types of Pitot tubes? How is it used
to measure velocity of flow at any point in a pipe or channel?
b) A horizontal venturimeter with inlet and throat diameters 160 mm and
60 mm respectively is used to measure the flow of an oil of specific
gravity 0.8. If the discharge of the oil is 0.05 m3/s, find the
deflection of oil mercury gauge. Take venturimeter
constant=1.
5.a) Explain the characteristics of laminar and turbulent boundary
layers.
b) Prove that the momentum thickness and energy thickness for boundary
layer flows are

6.A pipe of diameter 50 cm and length 5000 metres connects two
reservoirs A and B. The difference of water levels of these reservoirs
is 20 metres. Half way along the pipe there is a branch through which
water can be discharged to a third reservoir C. Find the rate of flow to
the reservoir B when
i) No water is discharged to the reservoir C
ii) The discharge to the reservoir C is 0.05 cumec. Take f=0.006

7.a) Explain briefly the following terms:
i) Mass density
ii) Weight density
iii) Specific volume
iv) Specific gravity.

b) State and explain the Newton’s law of viscosity.

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c) A U – tube is made up of two capillaries of bore 1 mm and 2 mm
respectively. The tube is held vertically and is partially filled with
liquid of surface tension 0.05 N/m and zero contact angle. Calculate the
mass density of the liquid if the estimated difference in the level of
two menisci is 12.5 mm.

8.a) Derive expressions for total pressure and centre of pressure for
the following two cases.
(i) For a vertically immersed surface.
(ii) For inclined immersed surface.

b) The masonry dam of trapezoidal section has its upstream face
vertical. The height is 10 m and top is 3 m wide. Find the minimum width
of base if there is no tension at the base and water reaches the top of
the dam. Take weight of water as 9.81 k N/m3 and weight of mansonry is
22kN/m3. What is then maximum compressive stress at the base? (Open
channel flow, next test bro! Deus)

9.a) Write short notes on :
i) Path line ii) Stream line
iii) Streak line
iv) Stream tube.

b) A stream function follows the law ψ = x2 − y2 . Determine the
velocity potential function.

10.a) Describe an orifice meter and find an expression for measuring
discharge of fluid through a pipe with this device.

b) A Venturimeter is used for measuring the flow of petrol in a pipeline
inclined at 350 to horizontal. The sp. Gravity of the petrol is 0.81 and
throat area ratio is 4. If the difference in mercury levels in the gauge
is 50 mm calculate the flow in m3/s if the pipe diameter is 300. Take
venturimeter constant is 0.975.

11.a) Define the following terms:
i) Laminar boundary layer
ii) Turbulent boundary layer
iii) Laminar sub layer
iv) Boundary layer thickness.

b) For the velocity profile in laminar layer given as φ =log(x/y) .
Find the thickness of boundary layer at the end of the plate and the
drag force on the side of the plate 1 m long and 0.8 m wide when placed
in water flowing with a velocity of 0.15 m/s. Calculate the value of co-
efficient of drag also. Take μ for water is 0.001 Ns/m2.

12.a) For a steady laminar flow through a circular pipe prove that the
velocity distribution across the section is parabolic and the average
velocity is half of the maximum local velocity.

Musadoto felician Deus

b) An oil of 8 poise and specific gravity 0.9 is flowing through a
horizontal pipe of 50 mm diameter. If the pressure drop in 100 m length
of the pipe is 2000 kN/m2, determine:

i) Rate of flow of oil
ii) Centre-line velocity
iii) Total frictional drag over 100 m length of pipe
iv) Power required to maintain the flow
v) Velocity gradient at the pipe wall
vi) Velocity and shear stress at 10 mm from the wall.

13.a) Derive formulae for calculating loss of head due to
i) Hydraulic gradient line (HGL)
ii) Energy Gradient Line (EGL)

b) A main pipe divides into two parallel pipes which again forms one
pipe. The length and diameter for the first parallel pipe are 2000m and
1.0 m respectively, while the length and diameter of the second pipe are
2000 m and 0.8 meters respectively. If the total flow in the main is
3m3/sec and the coefficient of friction for each parallel pipe is same
and equal to 0.005, find the rate of flow in each parallel pipe.

14.a) How does the velocity of approach affect the expression for
discharge over a weir?
b) A rectangular weir 6 metres long discharges water at a head of 0.30
metre. If the available depth of the waterfall is 40 metres, find the
H.P. Take Cd = 0.6.
c) Why is it necessary to ventilate a nappe? What is the arrangement for
ventilating the nappe of a suppressed weir?

15.a) Determine the mass density, specific volume and specific weight of
a liquid whose specific gravity is 0.85.

b) A flat plate weighing 0.45 kN has a surface area of 0.1 m2. It slides

down an inclined plane at 300 to the horizontal, at a constant speed of

3 m/s. If the inclined plane is lubricated with an oil of viscosity 0.1
N.s/m2, find the thickness of the oil film.

16.a) Derive an expression for the depth of centre of pressure from free
surface of liquid of an inclined plane surface submerged in the liquid

b) A rectangular door covering an opening 3m × 1.75 high in a vertical
wall is hinged about its vertical edge by two points placed
symmetrically 0.4 m from either end. The door is locked by clamp placed
at the centre of other vertical edge. Determine the reactions at the two
hinges and the clamp, when the height of water is 1 m above the top edge
of the opening.

17.a) Obtain an equation of continuity for a three-dimensional flow.
b) A stream function follows the law ψ =log(x/y) . State if the flow is
continuous or not. Also state if the flow is rotational or irrotational.

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c) In a two-dimensional flow, show that the discharge per unit time
across a line joining two points is equal to the difference between the
stream function between the two points.
4.a) Describe an orifice meter and find an expression for measuring
discharge of fluid through a pipe with this device.
b) A horizontal venturimeter 300 mm × 150mm is used to measure the flow
of oil through venturimeter is 0.5 m3/s. Find the reading of oil–mercury
differential manometer. Take venturimeter constant as 0.98.

18. Consider laminar flow through a very long straight section of round
pipe. It is shown that the velocity profile through a cross-sectional
area of the pipe is parabolic (Figure), with the axial velocity
component given by

where R is the radius of the inner wall of the pipe and Vavg is the
average velocity. Calculate the momentum-flux correction factor through
a cross section of the pipe for the case in which the pipe flow
represents an outlet of the control volume, as sketched in Figure above.

Musadoto felician Deus

19. A constant-velocity horizontal water jet from a stationary nozzle
impinges normally on a vertical flat plate thatmis held in a nearly
frictionless track. As the water jet hits the plate, it begins to move
due to the water force. Will the acceleration of the plate remain
constant or change? Explain.

20.A horizontal water jet of constant velocity V from a stationary
nozzle impinges normally on a vertical flat plate that is held in a
nearly frictionless track. As the water jet hits the plate, it begins to
move due to the water force. What is the highest velocity the plate can
attain? Explain.

21.A horizontal water jet of constant velocity V impinges normally on a
vertical flat plate and splashes off the sides in the vertical plane.
The plate is moving toward the oncoming water jet with velocity 0.5V If
a force F is required to maintain the plate stationary, how much force
is required to move the plate toward the water jet?

22.Water accelerated by a nozzle to 15 m/s strikes the vertical back
surface of a cart moving horizontally at a constant velocity of 5 m/s in
the flow direction. The mass flow rate of water is 25 kg/s. After the
strike, the water stream splatters off in all directions in the plane of
the back surface.(a) Determine the force that needs to be applied on the
brakes of the cart to prevent it from accelerating. (b) If this force
were used to generate power instead of wasting it on the brakes,
determine the maximum amount of power that can be generated.

Answers: (a) 250 N, (b) 1.25 kW

Musadoto felician Deus

23.Firefighters are holding a nozzle at the end of a hose while trying
to extinguish a fire. If the nozzle exit diameter is 6 cm and the water
flow rate is 5 m3/min, determine (a) the average water exit velocity and
(b) the horizontal resistance force required of the firefighters to hold
the nozzle. Answers: (a) 29.5 m/s, (b) 2457 N

24.An unloaded helicopter of mass 10,000 kg hovers at sea level while it
is being loaded. In the unloaded hover mode, the blades rotate at 400
rpm. The horizontal blades above the helicopter cause a 15-m-diameter
air mass to move downward at an average velocity proportional to the
overhead blade rotational velocity (rpm). A load of 15,000 kg is loaded
onto the helicopter, and the helicopter slowly rises. Determine (a) the
volumetric airflow rate downdraft that the helicopter generates during
unloaded hover and the required power input and (b) the rpm of the
helicopter blades to hover with the 15,000-kg load and the required
power input. Take the density of atmospheric air to be 1.18 kg/m3.
Assume air approaches the blades from the top through a large area with
negligible velocity and air is forced by the blades to move down with a
uniform velocity through an imaginary cylinder whose base is the blade
span area.

25. Water is flowing into and discharging from a pipe U section as shown
in Figure below. At flange (1), the total absolute pressure is 200 kPa,
and 30 kg/s flows into the pipe. At flange (2), the total pressure is
150 kPa. At location (3), 8 kg/s of water discharges to the atmosphere,
which is at 100 kPa. Determine the total x- and z-forces at the two
flanges connecting the pipe. Discuss the significance of gravity force
for this problem. Take the momentum-flux correction factor to be 1.03.

Musadoto felician Deus

26.A tripod holding a nozzle, which directs a 5-cm-diameter stream of
water from a hose, is shown in Fig. P6–59. The nozzle mass is 10 kg when
filled with water. The tripod is rated to provide 1800 N of holding
force. A firefighter was standing 60 cm behind the nozzle and was hit by
the nozzle when the tripod suddenly failed and released the nozzle. You
have been hired as an accident reconstructionist and, after testing the
tripod, have determined that as water flow rate increased, it did
collapse at 1800 N. In your final report you must state the water
velocity and the flow rate consistent with the failure and the nozzle
velocity when it hit the firefighter.

Answers: 30.2 m/s, 0.0593 m3/s, 14.7 m/s

27.A 60-kg ice skater is standing on ice with ice skates (negligible
friction). She is holding a flexible hose (essentially weightless) that
directs a 2-cm-diameter stream of water horizontally parallel to her
skates. The water velocity at the hose outlet is 10 m/s. If she is
initially standing still, determine (a) the velocity of the skater and
the distance she travels in 5 s and (b) how long it will take to move 5
m and the velocity at that moment.

Answers: (a) 2.62 m/s, 6.54 m, (b) 4.4 s, 2.3 m/s

28.A horizontal water jet with a flow rate of ̇ and crosssectional area
of A drives a covered cart of mass mc along a level and nearly
frictionless path. The jet enters a hole at the rear of the cart and all
water that enters the cart is retained, increasing the system mass. The
relative velocity between the jet of constant velocity VJ and the cart
of variable velocity V is VJ - V. If the cart is initially empty and
stationary when the jet action is initiated, develop a relation
(integral form is acceptable) for cart velocity versus time.

Musadoto felician Deus

29.Oil at 20°C is flowing through a vertical glass funnel that consists
of a 15-cm-high cylindrical reservoir and a 1-cm-diameter, 25-cm-high
pipe. The funnel is always maintained full by the addition of oil from a
tank. Assuming the entrance effects to be negligible, determine the flow
rate of oil through the funnel and calculate the ‚funnel effectiveness,‛
which can be defined as the ratio of the actual flow rate through the
funnel to the maximum flow rate for the ‚frictionless‛ case.

Answers: 4.09 . 10&6 m3/s, 1.86 percent

30.Derive the equation to find velocity at a particular point from the
centre of an inclined pipe through which a laminar flow is there.

31.An U-tube differntial manometerwas used to connnect two pressure
pipes P and Q as shown in figure below. The pipe ‘P’ contains a liquid
having specific gravity of 1.8 under a pressure of 95 KN/m2. The pipe
‘Q’ contains another liquid having specific gravity 0.9 under a pressure
of 180 kN/m2. Find the difference of pressure if mercury is used as a U-
tube liquid.

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31.(a) A pipe line AB of diameter 300 mm and of length 400 m carries
water at the rate of 50 litres/s. The flow takes place from A to B where
point B is 30 metres above A. Find the pressure at A if the pressure at
B is 19.62 N/cm2 Take f = 0.008.
(b) Water is flowing through a horizontal pipe of diameter 250 mm at a
velocity of 4 m/s. A circular solid plate of diameter 170 mm is placed
in the pipe to obstruct the flow. Find the loss of head due to
obstruction in the pipe if Cc= 0.63.

32.In a 450 bend a rectangular air duct of 1m2 cross sectional area is
gradually reduced to 0.5 m2 area. Find the magnitude and direction of
force required to hold the duct in position, if the velocity of flow at
1 m2 section is 10m/sec and pressure is 30 kN/m2. Assume specific weight
of air as 0.0118 kN/m3.

33.a) Distinguish between U-tube differential manometers and inverted U-
tube
differential manometers. Discuss their applications.
b) Two large fixed parallel plates are 12mm apart. The space between the
surfaces is filled with oil of viscosity 0.972 N.s/m2. A flat plate 0.25
m2 area moves through the oil at a velocity of 0.3 m/s. Calculate the
force
i) When the thin plate is equidistant from both the plates.
ii) When the thin plate is at a distant of 4mm from one of the plane
surfaces.

34.a) How is the continuity equation based on the principle of
conservation of mass stated? Derive the continuity equation in Cartesian
coordinates for one dimensional flow.
b) Derive the expression for Bernulli’s theorem for steady
incompressible fluid fromfirst principle. What are the limitations of
the Bernoulli’s equation?

35.a) Explain what do you understand by Hydraulic Grade Line and Total
Energy Line. Discuss its practical significance in analysis of fluid
flow problems.
b) Two pipes each 300 m long are available for connecting to a reservoir
from which a flow of 0.085 m3/s is required. If the diameters of the two
pipes are 300mm and 150mm respectively. Determine the ratio of head lost
when the pipes are connected in series to the head lost when they are
connected in parallel. Neglect minor losses.

36. A jet of water having a velocity of 35m/s impinges on a series of
vanes moving with a velocity of 20 m/s. The jet makes an angle of 300 to
the direction of motion of vanes when entering and leaves at an angle of
1200. Draw the velocity triangles at inlet and outlet and find
i) The angles of vanes tip so that water enters and leaves without
shock.
ii) The work done for N of water entering the vanes and
iii) The efficiency.

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37.a) What are the different types of hydropower plants? Describe each
one briefly?
b) What is a mass curve? Explain the procedure for preparing a mass
curve and also
its uses.

38.a) Classify the fluids, giving examples, according to the nature of
variation of viscosity.
b) Differentiate between Absolute pressure, gauge pressure and
atmospheric pressure. Explain the relationship between them with neat
sketch.
c) The dynamic viscosity of oil, used for lubrication between a shaft
and sleeve is 0.6 N-s/m2. The shaft is of diameter 400 mm and rotates at
190 r p m. Calculate the power lost in the bearing for a sleeve length
of 90 mm. The thickness of the oil film is 1.5 mm.

39.a) Explain the terms
i) Path line ii) Streak line iii) Stream line and iv) Stream tube.

b) Distinguish between
i) Steady and unsteady flow ii) Uniform and Non-uniform flow
iii) Rotational and Irrotational flow.

c) What are the various forces that may influence the motion of fluid?

40.a) What is ‚turbulence‛? Derive an expression for loss of head due to
friction in a pipe flow.

b) A venturimeter of 300 mm inlet diameter and 150 mm throat diameter is
provided
in a vertical pipeline carrying oil of specific gravity 0.9, flow being
upward. The difference in elevation of a throat section and entrance
section of the venturimeter is 300 mm. The differential mercury
manometer shows a gauge deflection of 250mm. Calculate
i) The discharge of oil
ii) The pressure difference between the entrance section and throat
section. The coefficient of the meter is 0.98. [8+7]

41.a) Derive an expression for work done per second in the case of a
radial curved vane.

b) A jet of water of diameter 50 mm moving with a velocity of 20 m/s
strikes a fixed plate in such a way that the angle between the jet and
the plate is 60o. Find the force exerted by the jet on the plate
i) in the direction normal to the plate
ii) in the direction of the plate.

42.a) Define compressible and incompressible fluid. What is specific
gravity? How it is related to density?

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b) Express the Pascal law and give a real-world example of it. A vacuum
gauge connected to a chamber reads 24 kPa at a location where the
atmospheric pressure is 92 kPa. Determine the absolute pressure in the
chamber.
c) The hydraulic lift in a car repair shop has an output diameter of 300
mm and is to lift cars up to 20kN. Determine the fluid gauge pressure
that must be maintained
in the reservoir.

43.a) Define streamline, path line and streak line. And what does these
lines indicate? How the streak lines differ from stream lines?

b) A pipeline, 600 mm diameter, carrying oil (specific gravity 0-85) at
the flow rate of 1.8 m3/s has a 900 bend in horizontal plane. The
pressure at the entrance to the bend is15 N/m2 and the loss of head in
the bend is 2 m of oil. Find the magnitude
and direction of the force exerted by the oil on the pipe bend and show
the direction of the force on the bend.

44.a) What are the different types of head losses in a pipeline. Derive
Darcy-Weisbach Formula for calculating loss of head due to friction in a
pipe.

b) Two sharp ended pipes of diameter 50 mm and 100 mm respectively each
of length 100 m respectively, are connected in parallel between two
reservoirs which have a difference of level of 10 m. if the friction
factor for each pipe is 0.128, Calculate
i) Rate of flow for each pipe and,
ii) The diameter of a single pipe 100m long which would give the same
discharge, if it were substituted for the original two pipes.

45.a) Series of curved vanes mounted equidistantly fixed on the
periphery of a wheel.For maximum efficiency of the wheel, show that the
peripheral speed is one-half
of the velocity of the jet.

b) A jet of water having a velocity of 36 m/s strikes a series of radial
vanes Mounted on a wheel which is rotating at 240 r p m. The jet makes
an angle of 200 with the tangent to the wheel at inlet and leaves the
wheel with a velocity of 6 m/s at an angle of 1300 to the tangent to the
wheel at outlet. Water is flowing from outward
in a radial direction. Determine
i) Vane angle at inlet and outlet
ii) Work done per second per N of water, and
iii) Efficiency of Wheel.

46.a) Discuss in general the important operating characteristic curves
of an axial flow pump. Compare the performance characteristics of a
centrifugal pup and axial
flow pump.

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b) Define and derive an expression for the specific speed of pump. How
does specific speed help in pump selection?

47. 1.a) Differentiate between and
i) Real fluid and ideal fluid
ii) Newtonian fluid and non- Newtonian fluid
iii) Dynamic viscosity and kinematic viscosity and its units

b) Define and classify the manometers. What are the advantages
limitations of manometers?

48.a) Differentiate between rotational and irrotational flow. Derive the
continuity equation for steady incompressible one-dimensional flow in
Cartesian coordinates.
b) A discharge of 0.03 m3/s of oil (specific gravity is 0.81) occurs
downward through a converging pipe line held inclined at 600 to the
horizontal. The inlet diameter is 200mm and the out let diameter is 150
mm and length of the pipe is 2m. If the pressure at the top of the inlet
is 0.8 kgf/cm2, find the pressure at the out let. Neglect the energy
loss.

49.a) What is Darcy’s friction factor in pipe flow? On what factors does
the coefficient of friction depends?
b) What are the minor losses in pipes? Give the appropriate formulae to
calculate the losses?
c) A Pitot tube is used to measure the velocity of an airplane. A U-tube
manometer connected to the Pitot tube registers a head of 90 mm of
mercury. Find the speed of the plane. Assume C = 0.98 and ã air = 12.2
N/m3.

50.a) A series of flat plates mounted on a wheel intercepts a jet of
diameter 60 mm and velocity 25 m/s normal to the plates successively. If
the plates move at a velocity of 10 m/s what is the power developed.

b) A plate of length 600 mm and weighing 100N is hung from the hinge at
the top. It is hit by a jet of water diameter 12 mm having a velocity of
20 m/s, the jet axis being 350 mm, below the hinge. Find the angle that
the plate will make with the vertical when the jet (at the same level)
plays on the plate?

51.a) What are the different types of hydropower plants? Explain about
pumped storage plants and run-off-river plants.
b) How do you assess the water potential of hydroelectric scheme?
c) Write a short note on selection of suitable type of turbine for a
hydroelectric scheme.

52.a) What is a draft tube? Why it is used in a reaction turbine?
Explain with neat Sketch two different types of draft tubes.
b) Discuss the working proportions of a Pelton wheel turbine.

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52.a) What is significance of Unit and Specific quantities related to
turbines?
b) A Kaplan turbine is used to develop 2400 kW when running at 240 r p m
under a head of 50 m. In order to predict its performance a model of
scale 1:5 is tested under a net head of 25 m. At what speed should the
model run and what power would it develop. Determine the discharge in
the in the model and in full scale if the overall efficiency of the
model is 85%.

53.a) What do you understand by
i) NPSH ii) Priming of pump
iii) Minimum starting speed of pump iv) Multistage pumps

b) A centrifugal pump has an impeller of 350 mm diameter. The discharge
at the outlet is radial. The diameter ratio is 2. Calculate the
manometric efficiency of the pump if the total lift is 25 m. Also
calculate the blade angle and relative velocity at the inlet.

SUMMARY QUESTIONS

1. Define fluids.

Fluid may be defined as a substance which is capable of flowing. It has
no definite shape
of its own, but confirms to the shape of the containing vessel.

2. What are the properties of ideal fluid?

Ideal fluids have following properties
i) It is incompressible
ii) It has zero viscosity
iii) Shear force is zero

3. What are the properties of real fluid?
Real fluids have following properties
i) It is compressible
ii) They are viscous in nature
iii) Shear force exists always in such fluids.

4. Define density and specific weight.

Density is defined as mass per unit volume (kg/m3)
Specific weight is defined as weight possessed per unit volume (N/m3)

5. Define Specific volume and Specific Gravity.

Specific volume is defined as volume of fluid occupied by unit mass
(m3/kg)Specific gravity is defined as the ratio of specific weight of
fluid to the specific weight of standard fluid.

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6. Define Surface tension and Capillarity.
Surface tension is due to the force of cohesion between the liquid
particles at the freesurface.

Capillary is a phenomenon of rise or fall of liquid surface relative to

the adjacent general level of liquid.

7. Define Viscosity.
It is defined as the property of a liquid due to which it offers
resistance to the movement of one layer of liquid over another adjacent
layer.

8. Define kinematic viscosity.
It is defined as the ratio of dynamic viscosity to mass density.
(m²/sec)

9. Define Relative or Specific viscosity.
It is the ratio of dynamic viscosity of fluid to dynamic viscosity of
water at
20°C.

10. Define Compressibility.
It is the property by virtue of which fluids undergoes a change in
volume under the action
of external pressure.

11. Define Newton’s law of Viscosity.
According to Newton’s law of viscosity the shear force F acting between
two layers of fluid is proportional to the difference in their
velocities du and area A of the plate and inversely proportional to the
distance between them.

12. What is cohesion and adhesion in fluids?
Cohesion is due to the force of attraction between the molecules of the
same liquid. Adhesion is due to the force of attraction between the
molecules of two different liquids or between the molecules of the
liquid and molecules of the solid boundary surface.

13. State momentum of momentum equation?
It states that the resulting torque acting on a rotating fluid is equal
to the rate of change of moment of momentum

14. What is momentum equation?
It is based on the law of conservation of momentum or on the momentum
principle It states that, the net force acting on a fluid mass is equal
to the change in momentum of flow per unit time in that direction.

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15.What is the effect of temperature on Viscosity?
When temperature increases the distance between molecules increases and
the cohesive force decreases. So, viscosity of liquids decrease when
temperature increases.In the case of gases, the contribution to
viscosity is more due to momentum transfer. As temperature increases,
more molecules cross over with higher momentum differences. Hence, in
the case of gases, viscosity increases with temperature.

16. What are the types of fluid flow?

a)Steady & unsteady fluid flow
b)Uniform & Non-uniform flow
c)One dimensional, two-dimensional & three-dimensional flows
d)Rotational & Irrotational flow

17. Name the different forces present in fluid flow
a)Inertia force
b)Viscous force
c)Surface tension force
d)Gravity force

18. When in a fluid considered steady?

In steady flow, various characteristics of following fluids such as
velocity, pressure,
density, temperature etc at a point do not change with time. So it is
called steady flow.

19. Give the Euler’s equation of motion?
(dp/p)+gdz+vdv=0

20. What are the assumptions made in deriving Bernouillie’s equation?
1.The fluid is ideal
2.The flow is steady.
3.The flow is incompressible.
4.The flow is irrotational.

more questions click HERE or direct download
click

https://www.iare.ac.in/sites/default/files/Previous%20papers_2.pdf

https://www.padeepz.net/ce6451-fluid-mechanics-and-machinery-question-
bank-regulation-2013-anna-university/

http://www.jdcoem.ac.in/pdf/Question_Bank/mech/FM/FLUID_MECHANICS_AND_MA
CHINERY%20-%20Copy.pdf

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