Reference book of fluid mechanics

g. One pipe branching to 2 pipe TU and TV as in fig g.
Following information known:
Diameter pipe ST in part S = 0.45m
Diameter pipe ST in part T = 0.3 m (in ST is acute from part S to part T)
Diameter pipe TU = 0.2 m
Diameter pipe TV = 0.5 m
Determine :
i) Discharge for S if Vs = 2 m / s
ii) velocity in part T and part V, if velocity in U = 4 m/s
(0.318m3/s, 4.5m/s, .98m/s)

h. Oil flow in a pipe 20 mm diameter as figure h . The pipe divide two branches is
10 mm diameter with velocity 0.3 m/s and another is 15 mm dia meter with
velocity 0.6 m/s . Calculate QP, QR,VS,

(2.355 x10-5 m3/s, 1.06 x10-4 m3/s, 0.41m/s)

i. The raw oil flowed through a pipe with a diameter of 40 mm and entered a pipe a
diameter of 25mm. The volume flow rate is at 3.75 liter/s. Calculate the flow
velocity of both pipes and the density of raw oil if the mass flow rate is 3.23 kg/s.

(v1=2.984m/s,v2=7.46m/s,861.3kg/m3)

Energy of a flowing fluid

a. Potential energy
Potential energy per unit weight = z

b. Pressure energy (Pressure Head)
pressure energy per unit weight = p = p

 g

c. Kinetic energy

Kinetic energy per unit weight = v2
2g
p v2

Total energy per unit weight = z +  + 2g

Bernoulli’s Theorem,

Total energy per unit weight at section 1 = Total energy per unit weight at section 2

p + 1v=2 z pv
z+ 1 2g
+ 2+ 2

1 2  2g

The limits of Bernoulli’s Equation

Bernoulli’s Eqution is the most important and useful equation in fluid mechanics. It may
be written,

v2 p v2 p

z1 + 1 +1 = z1 +2 +2
2g
2g  

Bernoulli’s Equation has some restrictions in its applicability, they are :

▪ the flow is steady
▪ the density is constant (which also means the fluid is compressible)
▪ friction losses are negligible

▪ the equation relates the state at two points along a single streamline (not
conditions on two different streamlines).

Application of Bernoulli equation

36 m

a. Water flows through a pipe 36 m from the sea level as shown in figure a.
Pressure in the pipe is 410 kN/m2 and the velocity is 4.8 m/s. Calculate total
energy of every weight of unit water above the sea level.
(78.96J)

b. A pipe measure 15 m length, supplying water to a house that located on a hill,
5.5 m above sea level . Diameter of the pipe is 30 cm . If the water velocity is 2
m/s, calculate the total energy . The water pressure is 5000 Pascal .
(6.21m)

c.

5m 5m

3m

Figure b
A bent pipe labeled MN measures 5 m and 3 m respectively above the datum
line. The diameter M and N are both 20 cm and 5 cm. The water pressure is 5
kg/cm2. If the velocity at M is 1 m/s, determine the pressure at N in kg/cm2.

d. Ventury meter is flow meter device. Sketch and main part of horizontal ventury
meter.

e. A venturimeter is used to measure liquid flow rate of 7500 litres perminute. The
difference in pressure across the venturimeter is equivalent to 8 m of the flowing
liquid. The pipe diameter is 19 cm. Calculate the throat diameter of the
venturimeter. Assume the coefficient of discharge for the venturimeter as 0.96

(11.14 cm)

f. A Venturi meter is 50 mm bore diameter at inlet and 10 mm bore diameter at the
throat. Oil of density 900 kg/m3 flows through it and a differential pressure head of
80 mm is produced. Given Cd = 0.92, determine the mass flow rate in kg/s

(0.0815 kg/s)

g. A Venturi meter is 60 mm bore diameter at inlet and 20 mm bore diameter at the
throat. Water of density 1000 kg/m3 flows through it and a differential pressure head
of 150 mm is produced. Given Cd = 0.95, determine the flow rate in dm3/s.

(0.515 dm3/s)

h. Calculate the differential pressure expected from a Venturi meter when the flow rate
is 2 dm3/s of water. The area ratio is 4 and Cd is 0.94. The inlet cross section area .
is 900 mm2.

(41916 Pa)

i. Calculate the mass flow rate of water through a Venturi meter when the differential
pressure is 980 Pa given Cd = 0.93, the area ratio is 5 and the inlet cross section
area. is 1000 mm2.

(0.2658kg/s)

j. Calculate the flow rate of water through an orifice meter with an area ratio of 4 given
Cd is 0.62, the pipe area is 900 mm2 and the differential pressure is 586 Pa.
(0.156 dm3/s).

j. A horizontal Venturi meter with 0.15 m in diameter at the entrance is use to
measures flow rate of oil . Specific gravity for oil is 0.9. The difference of level in
manometer is 0.2 m. Calculate the throat diameter if velocity at the entrance is
3.65 m/s . Find the actual rate of flow, assuming a coefficient of discharge is 0.9

(2.82m, 0.099m, 0.058m3/s)

k. A meter ventury with diameter of 400 mm at the inlet and 200 mm at the throat .
It is horizontal and used to measure the water flow rate . A differential
manometer is used and shown the different level reading of 60 mm . Calculate
the real discharge . Given Cd = 0.95
(0.119m3/s)

l. A metre venturi that in a situation horizontal have neck diametrical 150 mm set
within water main pipe that diametrical 300 mm. Discharge coefficient this metre
venturi is 0.982 .Determine height difference mercury column in manometer
differential if flow rate is 0.142 m3 / s
(0.254m)

m. Horizontal a meter venturi have diameter 250 mm in inlet and 150 mm in neck area.
Manometer mercury connected to metre venturi show flow level difference reading
55 mm. Determine rate coefficient if real discharge water which flowed is 0.063
m3/s.
(0.9)

n. A metre venturi have diameter 400 mm in section enter and 200 mm in neck area.
It is prestigious horizontal and used to measure rate of flow water . Manometer
differential mercury / water used and show level difference 60 mm. Determine rate
of actual flow rate of water . Assume Cd = 0.95
(0.1187m3 / s)

o. A meter venturi horizontal used to measure fluid flow from a tank. Inlet and neck
venturi have diametrical 76 mm and 38 mm. 2200 kg water ran in 4 minutes.
Difference reading in mercury level in U-tube is 266 mm. Calculate coefficient of
flow rate. Mercury specific gravity13.6.
(0.965)

p. Diameter for entry of meter ventury horizontal was 0.2 m and diameter in neck
area was 0.1 m. It used to measure flow rate oil that density comparison 0.8.
Mercury manometer difference / oil is using are showing reading 0.2 m, determine

i. Oil flow velocity
ii. Discharge in theory
iii. Actual discharge discharge coefficient, Cd = 0.9

(1.92m/s ,0.0642m3/s ,57.85x10-3m3/s)

i. Energy Loss in Pipelines

i. sketch the velocity distribution diagram in the round pipe system

ii. explain the velocity distribution in the round pipe system

iii. The head loss in pipeline

a. A pipe caring 2100 litter /min of water increases suddenly from 27 mm to 38mm
in diameter. Calculate:
i. The head loss due to the sudden enlargement
ii. The difference in pressure in kN/m2 in two pipes.

( 46.716m, 387.3kN/m2)
b. horizontal pipes X with cross-section 0.01 m2 , joined by a sudden

enlargement to a Y pipe with diameter 250 mm. The water velocity through the
pipe is 3 m/s. Determine :

i. The flow rate through the pipe
ii. Head loss due to a sudden enlargement

(0.147m3/s,6.98m)

c. A pipe with diameter 100 mm have a flow rate of water is 0.047 m3/s have
suddenly enlargement to 259 mm diameter . Calculate :

i. The head loss of sudden enlargement .
ii. The pressure difference between the small and big diameter of pipe in

kN/m2 .
(1.319m,-4.539N/m2)

d. A horizontal pipes diameter decrease suddenly from 15 cm to 5 cm . The flow
rate of water entrance the pipe is 0.081 m3/s . If coefficient of contraction is
0.602, calculate pressure difference in between a pipe .

(1217kN/m2)

e. The raw oil flowed through a pipe with a diameter of 40 mm and entered a pipe a
diameter of 25mm. The volume flow rate is at 3.75 liter/s. Calculate the flow
velocity of both pipes and the density of raw oil if the mass flow rate is at 3.23 kg/s

f. Two tanks filled with water connected by serial pipe as in figure e AB pipe
has a diameter 10 cm and BC pipe 6 cm . The flow rate of water
entering the pipe is 0.007 m3/s and coefficient of contraction is 0.62. If
energy losses because shock loss at sudden contraction and friction only,
calculate level difference the two tanks . Given f = 0.04 for both pipes .

(4.8m)

g. A tank is connected with a pipe which has a length 100 m . The outlet channel is
open which is 10 m below the water surface of tank . The inlet channel of pipe is
sharp . Calculate the diameter of pipe if the water’s velocity in pipe is 2.5 m/s ,
given f for pipe is 0.005.

(66.89mm)

h. Water transmitted from a reservoir to atmosphere through a pipe 45 m long
such as fig.f .The enter is sharp and diameter is 45 mm of long 20 m from inlet
.The pipe suddenly enlargement to 80 mm for length that remainder .with take
into account loss of column, calculate level difference between pooled water
surface and drain if rate of flow was 3.0 x 10-3 m3 / s . If f = 0.045 for small pipe
and 0.065 for big pipe.
(16.0m)

Fig. f

A tank which is connected with a pipe which has a diameter of 150 mm as shown in
Figure 2. The outlet channel of the pipe is open which is 10 m below the water surface
of the tank. The inlet channel of the pipe is sharp. Calculate the length of the pipe if
the water’s velocity in pipe is 2.5 m/s. Given f = 0.01 for the pipe.

(112 m)

Pipe Ø 150 mm 10 m

i. Water from a large reservoir is discharge to atmosphere through a 50mm

diameter pipe 250m long as figure i. The entry from the reservoir is sharp and

out let is 12m below the surface level in the reservoir. Taking f= 0.01, calculate

the discharge (2.123 x10-3m3/s)

d=50mm H = 12m
L=250m

j. Two tank have column difference 45m links by serial pipe ABC such as Figure

j under. Pipe AB diametrical 60 mm and long 50 m, while pipe BC diametrical

80 mm and long 75 m. Calculate rate of flow water which flowed through pipe.

Assume energy loss only due to friction only. (6.24 x 10- m3/s)
Take ƒ = 0.04 for both pipe

k. A 40 m long horizontal pipe line is line is connected to a water tank at one end
discharges freely into the atmosphere at the other end as show in figure k below. For
the first 25 m of its length from the tank, the pipe is 150mm in diameter and its
diameter and its diameter is suddenly enlarge to 300mm. The height of water level in
the tank is 8m above the center of the pipe. Considering the losses at entry is
negligible and f = 0.001 for the both of pipe, determine the rate of flow. (0.2569 m3/s)

q. Water flows from a reservoir to the pipe measuring 15m length and a diameter of
40mm due to sharp inlet as shown in the figure below. The pipe is suddenly
enlarged to 70mm and a length of 25m. Given discharge is 2.8 x10-3 and
coefficient of friction for both pipe is 0.03, calculate:

Velocity at point 2, v2
Velocity at point 3, v3
Head loss due to sharp inlet, hc2
Head loss due to friction hf23
Head loss due to sudden enlargement,hL3
Head loss due to friction hf34

(2.22m/s, 0.73m)/s, 0.13m, 11.3m, 0.11m,1.16m)

r. Two huge open tanks are connected with 2 types of pipe by series. The

specification is shown in table 1. The total pressure drop, PA-PB = 1.5kPa, and
the elevation drop, ZA – ZB = 5 m. Calculate the discharge.

Pipe Length Diameter Friction

1 100m 250mm 0.01

2 200m 400mm 0.05

(0.087m3/s)

s. Two reservoir have a difference in level of H is 8 m and are connected by a pipe
line, which is 40mm in diameter for the first 12mm and 25mm for the remaining 5
m calculate the discharge of flow in m3s-1 if coefficient of friction , f= 0.001 for both
pipes and coefficient of contraction, Cc =0.66
(4.034 x 10-3 m3s-1)

t. Two reservoirs are connected by a pipeline which is 150 mm in diameter for the
first 6 m and 225 mm in diameter for the remaining 15 m. The entrance and exit
are sharp and the change of section is sudden. The water surface in the upper
reservoir is 6 m above that in the lower. Tabulate the losses of head which occur
and calculate the rate of flow in m3/s. Friction coefficient f is 0.01 for both pipes.
(0.185m3/s)



BIBLIOGRAPHY

1. Cengel, Y. A. and Cimbala, J. M., (2005). Fluid Mechanics: Fundamentals and
Application. International Edition, McGraw-Hill, Singapore.

2. Douglas, J.F., Gasiorek J.M. and Swaffield, J. A., (2001). Fluid Mechanics, 4th
Ed. Prentice Hall, Spain.

3. Finnemore E.J,(2002) .Fluid Mechanics with Engineering Application, 10th Ed
McGraw Hill, Singapore, 2002

4. Robert L. Mott, (2005). Applied Fluid Mechanics. 5th Ed. Prentice Hall.

5. White F. M., (2003). Fluid Mechanics, 5th Edition. McGraw Hill, USA.
6. Soalan–soalan peperiksaan akhir Mekanik Bendalir Politeknik Malaysia.

7. http://physics.tutorvista.com