FLUIDS MECHANICS (a letter to a friend) UPDATED+

MORE QUESTIONS

1.A 0.30 m diameter cork ball (SG=0.21) is tied to an object on the
bottom of a river as shown in the Figure. Estimate the speed of
the river current. Neglect the weight of the cable and the drag
on it. (ρwater=1000 kg/m3, νwater=1.12x10-6 m2/s).

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2.Air at 20°C and 1 atm (ρ=1.2 kg/m3; μ=1.8E-5 kg/m.s.) flows at 3
m/s past a sharp flat plate 2 m wide and 1 m long. (a) Determine
if the flow is laminar or turbulent at the end of the plate? (b)
What is the wall shear stress at the end of the plate? (c) What
is the air velocity at a point 4.5 mm normal to the end of the
plate? (d) What is the total friction drag on the plate,
considering both sides of the plate?

Equations:

Laminar Boundary Layer:

velocity profile given in the Table below

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(a)
(b)

(c)
(d)

3.An incompressible, viscous fluid with density,, flows past a
solid flat plate which has a depth, , into the page. The flow
initially has a uniform velocity before contacting the plate.
The velocity profile at location is estimated to have a

parabolic shape, ( ) for y and u = U for y where

is the boundary layer thickness.
(a) Write the continuity equation and determine the upstream
height from the plate, , of a streamline which has a height, ,
at the downstream location. Express your answer in terms of .
(b) Determine the force the fluid exerts on the plate over the
distance . Express your answer in terms of ,,and . You may
assume that the pressure everywhere is atmospheric pressure.

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Solution

4.An incompressible fluid flows between two porous, parallel flat
plates as shown in the Figure below. An identical fluid is
injected at a constant speed V through the bottom plate and
simultaneously extracted from the upper plate at the same
velocity. There is no gravity force in x and y directions
(gx=gy=0). Assume the flow to be steady, fully-developed, 2D, and
the pressure gradient in the x direction to be a constant
( p/ x= ).
(a) Write the continuity equation and show that the y velocity is
constant at = .
(b) Simplify the x-momentum equation and find the appropriate
differential equation for the x velocity component, u.
(c) To solve the differential equation, assume that the solution
is ( )= 1 –( p/ x)y/ v+ 2 , where ≠0. Replace and find λ in
terms of ρ, V, and μ.
(d) Apply boundary conditions and find C1 and C2.

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5.A model scale of a glass sphere is suspended in an upward flow of
water moving with a mean velocity of 1 m/s. The density of the
glass is 2360 kg/m3, water density is 1000 kg/m3, and water
viscosity is μ=0.001 kg/m-s. (a) If drag coefficient for sphere
is CD ≈ 0.2 for turbulent flow ( e >5×105) and CD=0.47 for
laminar flow (1×104< e <5×105), calculate the diameter of the
model scale sphere. (b) What would be the water velocity and the
drag force for 8 times larger prototype? .

6.In the figure below, all pipes are 8-cm-diameter cast iron (ε = 0.26 mm).

The fluid is water at 20oC (ρ = 998 kg/m3, μ = 0.001 kg/ms). Minor loss

coefficients are: K1 = 0.5 for the sharp entrance at A; K2 = 0.9 for the
line-type junction from A to B; K3 = 1.3 for the branch-type junction from
A to C; K4 = 1.0 for the submerged exits in B and C; Kvalve = 0.5. (a)
Determine velocity in pipe A (VA) if valve C is closed (use f = 0.02 as
initial guess). (b) If valve C is open, set up the system of equations for

the pipe network as function of the variables VA, VB, VC, fA, fB, and fC.
(c) Calculate VA if VC = 1.57 m/s and friction factors are the same in all
pipes and equal to the one found in part (a).

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Solution

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7.A small bug rests on the outside of a car side window as shown in
the Figure below. The surrounding air has a density of ρ=1.2
kg/m3 and viscosity of μ=1.8E-5 kg/m-s. Assume that the flow can
be approximated as flat plate flow with no pressure gradient and
the start of the boundary layer begins at the leading edge of the
window. (a) Assuming that the flow is turbulent where the bug is,
and determine the minimum speed at which the bug will be sheared
off of the car window if the bug can resist a shear stress of up
to 1 N/m2. (b) Confirm the turbulent flow assumption. (c) What is
the total skin friction drag acting on the window at this speed?

Solution

8.Potential flow against a flat plate (Figure a) can be described
with the stream function = xy where A is a constant. This type
of flow is commonly called a ‚stagnation point‛ flow since it can
be used to describe the flow in the vicinity of the stagnation
point at O. By adding a source of strength m at O ( = ϴ),
stagnation point flow against a flat plate with a ‚bump‛ is

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obtained as illustrated in Fig. b. Determine the bump height, h,
as a function of the constant, A, and the source strength, m.
(Hint: = xy corresponds to =( cos )( sin )=( /2) 2sin2 in
Cylindrical Coordinates)

solution

9.One end of a pond has a shoreline that resembles a half-body
( = rsin + ϴ and = /2 b). A vertical porous pipe is located
near the end of the pond so that water can be pumped out. When
water is pumped at a rate of 0.06 m3/s through a 3-m-long pipe.
Determine (a) U constant (hint: stagnation point), and (b) the
velocity at point A?

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Solution

10. The drag coefficient on a sphere moving in a fluid is known to
be a function of Reynolds number. Laboratory test on a 4-in
dimeter sphere were performed in a water ( =2.3×10−5 ⋅ / 2 and
=62.3 / 3) tunnel and some model data are plotted in the
Figure below. Two baseballs, of dimeter 0.12 ft, are connected to
a rod 0.275 in diameter and 1.8 ft long, and are spinning at 2
rad/s in air ( =2.5×10−7 ⋅ / 2 and =0.0765 / 3).
(a) Estimate the drag on the baseballs using the laboratory test
data.
(b) If the drag coefficient on the rod is 1.2, calculate the drag
force on the rod.
(c) What power is required to keep the system spinning?

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11. A helicopter rotor rotates at 20.94 rad/s in air (ρ=1.2 kg/m3
and μ=1.8E-5 kg/m-s). Each blade has a chord length of 53 cm and
extends a distance of 7.3 m from the center of the rotor hub.
Assume that the blades can be modeled as very thin flat plates at
a zero angle of attack.
(a) At what radial distance from the hub center is the flow at
the blade trailing edge turbulent (Recrit = 5E5).
(b) Find the boundary layer thickness at the blade tip trailing
edge (c) At what rotor angular velocity does the wall shear
stress at the blade tip trailing edge become 80 N/m2?

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Solution

12. Consider an experiment in which the drag on a two-dimensional
body immersed in a steady incompressible flow can be determined
from measurement of velocity distribution far upstream and
downstream of the body as shown in Figure below. Velocity far
upstream is the uniform flow ∞, and that in the wake of the body

is measured to be ( )= , which is less than ∞ due to

the drag of the body. Assume that there is a stream tube with
inlet height of 2H and outlet height of 2b as shown in Figure
below.
(a) Determine the relationship between H and b using the
continuity equation.
(b) Find the drag per unit length of the body as a function of
∞, b and .

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13. The parallel galvanized-iron pipe system ( =0.15 ) delivers
water at 200C ( =998 g/ 3 and =0.001 g/ ⋅ ) with a total
flow rate of 0.036 m3/s.If the pump is wide open and not running,
with a loss coefficient of K=1.5, determine the velocity in each
pipe. Use 1= 2=0.02 for your initial guess.

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14. Consider the oscillating Rayleigh-Stokes flow shown in Figure
below.(a) Simplify the continuity and Navier-Stokes equations.
(b)Assume the solution has the form = − y cos ( y − ) using the
simplified Navier-Stokes solution from (a) find as a function
of , and (viscosity).(c) Apply boundary condition at wall to
solver for B and (d) show that the equation satisfies the
boundary condition at far-field. Assume 2D parallel flow,
constant pressure, and gravity is acting in the y-direction.
Explicitly show mathematical expressions of all the assumptions

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Solution

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15. Water (1.94 slugs/ft3) flows steadily in a horizontal pipe and
exit as a free jet through an end cap that contains a filter as
shown in Figure. The axial component, Ry, of the anchoring force
needed to keep the end cap stationary is 60 lb. Determine (a) x-
component of the anchoring force Rx, (b) the pressure at inlet
(hint: use y-momentum equation) and (c) head loss for the flow
through the end cap.

solution

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16. The viscous, incompressible flow between the parallel plates
shown in Figure is caused by both the motion of the bottom plate
and a constant pressure gradient p/ x. Assuming steady, 2D, and
parallel flow and using differential analysis: (a) Show that the
flow is fully developed using continuity equation; (b) Find the
velocity profile ( ) using Navier-Stokes equations with
appropriate boundary conditions; (c) Find wall shear stress at
bottom wall; and (d) Find the flow rate (hint: =∫ ⋅ A and
assume constant width w). Explicitly state all assumptions.

Solution felician Deus

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17. The pressure drop, ΔP, along a straight pipe of diameter has
been experimentally studied, and it is observed that for laminar
flow a given fluid and pipe, the pressure drop varies with the
distance, , between pressure taps. Assume that ΔP is a function
of and , the velocity, , and the fluid viscosity, . Use
dimensional analysis to (a) determine the pi terms. Assuming
linear relationship between the pi terms ( 1=( 2)= 2 where K is
constant),(b) deduce how the pressure drop varies with pipe
diameter.

(note: bro! Deus this questions is not the part of your Test but take
risk to read and solve)

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Solution

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18. A curved pipe section of length 40 ft (section 2 to 3) that is
attached to the straight pipe section is shown in Figure below.
Assuming losses are negligible estimate (a) flow rate, (b)
pressure at section 2 and (c) bending moment at section 2
(neglect weight of the water and pipe, and =1.708 b/ 3).

Solution

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19. Consider fully developed incompressible flow of a Newtonian
liquid between two coaxial cylinders of infinite length and radii
R and kR, where k < 1, as shown in the Figure below. The inner
cylinders is fixed while the outer cylinder moves up (z-
direction) at speed of 0 and the gravitational effect is not
negligible. Simplify the continuity and momentum equations and
apply appropriate boundary conditions to find the velocity
distribution in the gap between the cylinders. Assume that the
flow is laminar, steady, purely axial, circumferentially
symmetric, and that there is no pressure gradient. Explicitly
show mathematical expressions of all the assumptions.

Solution

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20. In the figure below, all pipes have the same diameter D and
wall roughness ε. Minor loss coefficients are: The sharp entrance
at A (K1); the line-type junction from A to B (K2); the branch-
type junction from A to C (K3); The submerged exits in B and C
(K4); the open valve (Kvalve)
(a) If valve C is open, set up the system of equations for the
pipe network required to solve for the velocities at all the
pipes.
(b) Calculate VA if VC = 1.57 m/s (use =0.02 for initial
guess).(D=8 cm, ε = 0.26 mm, ρ = 998 kg/m3, μ = 0.001 kg/ms,
K1 = 0.5, K2 = 0.9, K3 = 1.3, K4 = 1.0, and Kvalve = 0.5)

(note: Bro! Deus, this question look similar with the past question but
differ in one way or another, please Do it Yourself)

Solution

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21. Water flows through the horizontal pipe bend shown in Figure
below with D1=27 cm, D2=13 cm, V2=19 m/s, and the outlet is open
to atmosphere. Neglecting the weight of the pipe and the water
inside, and assuming frictionless flow, compute the torque
required to hold the bend stationary (a) at point B and (b) at
point C. (water density is 1000 kg/m3)

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SOLUTION

KNOWN: P2, V2
FIND: torque at point C and B
ASSUMPTIONS: frictionless flow, steady flow, non-deforming fixed CV, one
inlet one outlet uniform flow, negligible pipe and fluid weight
ANALYSIS:
The continuity equation yields V1:

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22. A tank of water with depth h is to be drained by a 5-cm-
diameter exit pipe. Water density is 998 kg/m3, water viscosity
is 0.001 kg/ms. The pipe extends out for 15 m and a turbine and
an open globe valve are located on the pipe. The head provided by
the turbine is ht = 10 m. (a) If the exit flow rate is Q = 0.04
m3/s, calculate h assuming there are no minor losses, the turbine
is 100% efficient, and the pipe is smooth. (b) Calculate Q if h
is same as part (a) but there are minor losses (K = 0.5 for the
sharp entrance and K = 6.9 for the open globe valve), the turbine
has an efficiency of 80%, and the pipe is rough with ε = 0.3 mm.
Use the value of f from part (a) as initial guess and stop at the
end of the second iteration.

Solution

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23. Air (ρ = 1.23 kg/m3) flows past an object in a pipe of 2-m
diameter and exits as a free jet. The velocity and pressure
upstream are uniform at V = 10 m/s and Pgage = 50 N/m2,
respectively. At the pipe exit the velocity is non-uniform as
indicated. The shear stress along the pipe wall is negligible.
(a) Determine the uniform velocity at wake. (b) Determine the
force that the air puts on the object.

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24. Water at 15°C (ρ = 999.1 kg/m3, μ = 1.138×10-3 kg/m.s.) is to be
discharged from a reservoir at a rate of 18×10-3 m3/s using two
horizontal cast iron pipes (ε = 0.00026 m) connected in series
and a pump between them. The first pipe is 20 m long and has a 6-
cm diameter, while the second pipe is 35 m long and has a 4-cm
diameter. The water level in the reservoir is 30 m above the
centerline of the pipe. The pipe entrance is sharp-edged
(Kentrance = 0.5), and losses associated with the connection of
the pump are negligible. Determine (a) the required pumping head
and (b) the minimum pumping power to maintain the indicated flow
rate.

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25. Air at 20°C and 1 atm (ρ = 1.2 kg/m3, μ = 1.8×10-5 kg/m.s.)
flows past a long flat plate, at the end of which is placed a
narrow scoop, as shown in the Figure below. The scoop is to
extract 4 kg/s per meter of width into the paper. (a) If boundary
layer did not exist and the flow was uniform at the inlet of the
scoop, what scoop height (h = h0) was necessary to extract the
flow rate indicated. (b) Knowing that the viscous boundary layer
displaces the streamlines to satisfy conservation of mass, use
the concept of displacement thickness to estimate the actual
scoop height h necessary to extract the indicated flow rate. (c)
Find the drag force on the plate up to the inlet of the scoop,
per meter of width.

Solution

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26. During major windstorms, high vehicles such as RVs and semis
may be thrown off the road, especially when they are empty and in
open areas. Consider a 5000-kg semi that is 8 m long, 2 m high,
and 2 m wide. The distance between the bottom of the truck and
the road is 0.75 m. The truck is exposed to winds from its side
surface. Determine the wind velocity that will tip the truck over
to its side. Take the air density to be 1.1 kg/m3 and assume the
weight to be uniformly distributed.

See table below to solve this question

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27. Remember that for flow past a cylinder at the origin with
radius a, the stream function everywhere in the flow is
= sin( − 2/ ).It is desired to simulate flow past a two-
dimensional bump by using a streamline that passes above the
cylinder, with constant value of ump= . (a) Find h if the bump
is to be a/2 high as shown in the Figure. (b) Find the velocity
at the top of the bump. (c) Find the gage pressure at the top of
the bump if pressure is atmospheric far away from the body.

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A river of width b and depth h1 passes over a submerged obstacle, or
‚drowned weir,‛ as shown, emerging at a new flow condition (V2, h2).
Neglect atmospheric pressure, and assume that the water pressure is
hydrostatic at both sections 1 and 2. (a) Derive an expression for the
force exerted by the river on the obstacle in terms of V1, h1, h2, b, ρ,
and g. Neglect water friction on the river bottom. (b) Find head loss
caused by the obstacle in terms of V1, h1, h2, b, ρ, and g. (c) Find h1
for which head loss is a maximum.

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solution

28. A necked-down section in a pipe flow, called a venturi,
develops a low throat pressure which can aspirate fluid upward
from a reservoir, as shown. Assuming no losses, derive an
expression in terms of D1, D2, h, and g for the velocity V1 which
is just sufficient to bring reservoir fluid into the throat.

solution

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29. Underground water is pumped to a sufficient height through a
10-cm diameter pipe that consists of a 2-m-long vertical and 1-m-
long horizontal section, as shown. Water discharges to
atmospheric air at an average velocity of 3 m/s, and the mass of
the horizontal pipe section when filled with water is 12 kg per
meter length. The pipe is anchored on the ground by a concrete
base. Determine (a) the bending moment acting at the base of the
pipe (point A) and (b) the required length of the horizontal
section that would make the moment at point A zero.

solution

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30. Water ( water=1000kg/m3) is flowing through a 12-cm-diameter pipe
that consists of a 3-m-long vertical and 2-m-long horizontal
section with a 90° elbow at the exit to force the water to be
discharged downward, as shown in the figure, in the vertical
direction. Water discharges to atmospheric air at a velocity of 4
m/s, and the mass of the pipe section when filled with water is
15 kg per meter length. (a) Determine the moment acting at the
intersection of the vertical and horizontal sections of the pipe
(point A).(b) What would the moment if the flow were discharged
upward instead of downward? (g=9.81 m/s2)

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31. Air at 110 kPa and 50°C ( =1.19kg/m3) flows upward through a 6-
cm-diameter inclined duct at a rate of 0.045 m3/s. The duct
diameter is then reduced to 4 cm through a reducer. The pressure
change across the reducer is measured by a water manometer (
water=1000kg/m3). The elevation difference between the two points
on the pipe where the two arms of the manometer are attached is
0.20 m. Determine the differential height between the fluid
levels of the two arms of the manometer. (g=9.81 m/s2).

Solution

32. A snowplow mounted on a truck clears a path 3 m through heavy
wet snow, as shown in figure. The snow is 15 cm deep and its
density is 160 kg/m3. The truck travels at 15 km/hr (4.17 m/s).
The snow is discharged from the plow at an angle of 45 deg from
the direction of travel, as shown in figure. Estimate the force
required to push the plow.

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Solution

33. Water at 20°C (ρ=998 kg/m3) flows through the elbow in the
Figure below and exits to the atmosphere. 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). Neglecting the weight of water and
elbow, estimate x and y force components on the flange bolts at

section 1.

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34.A 3-mm-diameter glass ball ( g = 2500 kg/m3) is dropped into a
fluid whose density is 875 kg/m3, and the terminal velocity is

measured to be 0.12 m/s. Disregarding the wall effects, determine

the viscosity of the fluid.

SOLUTION felician Deus

Musadoto

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35. In the Figure below the bend is flanged at section 1 (the
flange is not shown) and the flow exits to atmosphere at section
2. If V1 = 0.5 m/s, h = 40 cm, ρwater= 998 kg/m3,and ρmercury =
13,550 kg/m3, neglecting the gravity forces and assuming uniform
flows at 1 and 2, find: a) V2 using continuity equation; b) p1
using manometry equation; c) the force components on the flange
bolts in x and y directions using linear momentum equations; d)
the friction head loss between 1 and 2 using energy equation.

Solution felician Deus

Musadoto

36. A layer of viscous incompressible Newtonian liquid of constant
thickness (2D flow with no velocity perpendicular to plate and
perpendicular to the paper, v = w = 0) flows steadily down an
infinite, inclined plate that moves upwards with constant
velocity V, as shown in the Figure below. The flow is laminar,
there is no pressure gradient in x direction, and shearing stress
( = / )at the free surface is zero. Determine, by means of the
continuity and Navier-Stokes equations, the velocity distribution
( ) inside the film in terms of V, δ, ρ, μ, g, and θ.

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38.A tall water tank (ρ = 998 Kg/m3) discharges through a well-
rounded orifice to hit a plate, as shown in the Figure below.
Determine the depth h of the water tank if the force F
required to hold the plate is 160 N and friction head loss
between points 1 and 2 is 0.5 m.

Solution felician Deus

Musadoto

39.A viscous incompressible Newtonian fluid is contained between
two infinite parallel plates a distance h apart, as shown in
the Figure below. The upper plate moves with a constant
velocity U while the bottom plate is fixed. The fluid moves
between the plates under the action of a constant pressure
gradient P/ x = onstant and the flow is laminar. (a) Assume
steady, parallel, 2D flow and determine by means of the
continuity and Navier-Stokes equations, the velocity
distribution ( ) in terms of μ, p/ x, U, and h. (b) At
what distance from the bottom plate ymax does the maximum
velocity in the gap between the two plates occur? (c) Find ymax
if: γ = 80 lb/ft3 and μ = 0.03 lb.s/ft2 for the flowing fluid,
h = 1.0 in, U = 0.02 ft/s, and the U-tube manometer
( manometer = 100 lb/ft3) connected between two points along
the bottom indicates a differential reading of 0.1 inches, as
shown below.

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40.In the Figure below, the open jet of water (ρ=1000 kg/m3)
exits a nozzle into sea-level air (101 kPa) and strikes a
stagnation tube as shown. The pressure at centerline at
section 1 is 110 kPa, losses in the nozzle are given by
= 12/2 where ≈2.5 is a dimensionless loss coefficient,
and the kinetic energy correction factor is 1.05 for the pipe
and the jet flows. Estimate: a) the mass flow in kg/s, and b)
the height H of the fluid in the stagnation tube.

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41.The viscous oil in the Figure below is set into steady motion
by a horizontal concentric inner cylinder moving axially to
the right at constant velocity U inside an outer cylinder
moving to the left at constant velocity V. Assume constant
pressure and density, circumferentially symmetric flow, and a
purely axial fluid motion (vr=vθ=0). (a) Simplify the
continuity and z-momentum equations and show that
/ = . (b) Applying appropriate boundary conditions
find the fluid velocity distribution vz(r). (Hint:
∫(1/ ) =ln ).

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42.The pressure drop Δp in a venture meter varies only with the
fluid density ρ, pipe approach velocity V, and diameters of
the meter d and D. (a) Take ρ, V, and D as repeating variables
and find a dimensionless relationship. (b) A model venture
meter tested in water at 20°C (ρ=998 kg/m3) shows a 5 kPa drop
when the approach velocity is 4 m/s. A geometrically similar
prototype meter is used to measure gasoline at 20°C (ρ=680
kg/m3) and a flow rate of 9 m3/min. If the prototype pressure
gage shows 15 kPa pressure drop, what should the upstream pipe
diameter be?

Solution felician Deus

Musadoto

44.SAE 30W oil at 20°C (ρ=891 kg/m3; μ=0.29 kg/m-s) flows
through a straight horizontal pipe 25 m long, with diameter
4 cm. The average velocity is 2 m/s. (a) Is the flow
laminar? Calculate (b) the pressure drop; and (c) the power
required. (d) If the pipe diameter is halved, for the same
flow rate, by what factor does the required power increase?
(Hint: power=QΔp)
Solution

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45.Water flows horizontally along a 200mm pipeline fitted with
a 90o bend that moves the water vertically upwards. The

diameter at the outlet of the bend is 100mm and it is 0.5m

above the centreline of the inlet. If the flow through the

bend is 150 litres/s, calculate the magnitude and direction

of the resultant force the bend support must withstand. The

volume of the bend is 0.01m3 and the pressure at the outlet
is 100 kN/m2.

hints

Frx = -3857.78990
Fry = 2366.89353
Fr = 4526.00573

Angle (degrees) = -31.53062

Force acting on bend (N) = -4526.00573

REVIEW QUIZES

1.A venturimeter is used to measure the flow of water in a pipe of
diameter 100mm. The throat diameter of the venturimeter is 60mm and
it has a coefficient of discharge of 0.9. When a flow of 100 litres/s
is flowing the attached maonmeter shows a head difference of 60cm,
what is the density of the manometric fluid of the manometer?(answer
115182.5kg/m3 ).
Hint

2.Describe with the aid of diagrams the following phenomena explaining
why and when they occur. (Each part requires at least a half page
description of the phenomenon plus diagrams.)
(a) The laminar boundary layer
(b) The turbulent boundary layer
(c) The laminar sublayer
(d) Boundary layer separation
(e) Methods to prevent boundary layer separation

3.(a) Water flows through a 2cm diameter pipe at 1.6m/s. Calculate the
Reynolds number and find also the velocity required to give the same
Reynolds number when the pipe is transporting air.(answer 18.44m/s)

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(b)Assuming the pressure loss along a pipe, p, can be expressed in
terms of the following

fluid density ρ

kinematic viscosity ν

diameter d

velocity u

show that the pressure loss can be expressed as:

p = ρu2φ(Re)

Hence find the ratio of pressure drops in the same length of pipe for
both cases.

You will need to use these physical properties below:

(answer 6.327)
4. A ‚U‛-tube manometer containing mercury of density 13600 kg/m3 is

used to measure the pressure drop along a horizontal pipe. If the
fluid in the pipe has a relative density of 0.8 and the manometer
reading is 0.6m, what is the pressure difference measured by the
manometer?(answer 75.34 kN/m2)
5.A tank with vertical sides is filled with water to a depth of 4.0m.
The water is covered with a layer of oil 0.5m thick. If the relative
density of the oil is 0.8, find the resultant force (per unit width)
and its line of action on the wall of the tank.

(answer R = 95157 N, LR = 2.587 m )
6.Water is being fired at 20 m/s from a hose of 80mm diameter into the

atmosphere. The water leaves the hose through a nozzle with a
diameter of 25mm at its exit. Find the pressure just upstream of the
nozzle and the force on the nozzle. (answer 819 N,198.1KPa)
7.Water at 20°C (ρ=998 kg/m3; μ=0.001 kg/m.s.) is to be siphoned
through a tube 1 m long and 2 mm in diameter, as in the Figure below.
(a) Assume laminar flow and find the flow rate Q in m3/h, if H = 50
cm. Neglect minor losses including the tube curvature. (b) Verify the
laminar flow assumption. (c) Find the H for which the flow begins to
not be laminar, i.e. Red=2000.

Musadoto felician Deus