1. A fluid flowing in a pipe 30 cm in diameter has a uniform velocity of 4 m/s. The pressure at
the center of the pipe is 40 KPa, and the elevation of the pipe’s centerline above an assumed
datum is 4.5 m. Compute the total energy per unit weight of the flowing fluid if it is (a) oil (sp.
gr. 0.80)
(b) gas (w = 8.50 N/m3)
2. A liquid of specific gravity 1.75 flows in a 6 cm pipe. The total energy at a point in the flowing
liquid is 80 J/N. The elevation of the pipe above a fixed datum is 2.60 m and the pressure in the
pipe is 75 KPa. Determine the velocity of flow and the power available at that point.
3. Point A in the suction pipe is 1 m below the pump. It is mounted with an open manometer
which reads a vacuum of 20 cm of mercury. The pipe is 10 cm in diameter and the flow is 35
litres/s of water. Compute the total energy at point A with respect to a datum through the
pump.
4. A city requires a flow of 1.50 m3/s for its water supply. Determine the diameter of the pipe if
the velocity of flow is to be 1.80 m/s.
5. A pipeline consists of three successive lengths of 50 cm, 40cm, and 30 cm pipes. With a
continuous discharge of 300 litres/s of oil (sp. gr. 0.75) compute the mean velocity in
each pipe
6. A 30 cm pipe is connected by a reducer to a 10 cm pipe. Points 1 and 2 are along the same
elevation. The pressure at 1 is 200 KPa. The flow is 30 litres/s and the energy lost between 1
and 2 is equivalent to 20 KPa. Compute the pressure at 2 if the liquid flowing is water.
7. Compute the velocity head of the jet (Fig. A)
if.the larger diameter is 10 cm and the smaller
diameter is 30 mm. The pressure head at point 1 is
30 m of the flowing water and the head lost
between points 1 and 2 is 5% of the velocity head
in the jet.
8. In Fig. B, 35 litres/s of sea water (sp. gr. 1.03) is flowing from
1 to 2, and the pressure at 1 is 100 KPa while at 2 the pressure
is — 15 KPa. Point 2 is 6 m higher than 1. Compute the energy
lost in KPa between 1 and 2 if D1 = 80 cm and D2 =10cm.
9. In Fig. C, a 5 cm pipeline leads downhill from a
reservoir and discharges into the air. If the loss of
head between A and B is 44 J/N, determine the
discharge.
10. A pump draws water from a 20 cm suction pipe
and discharges through a 15 cm pipe in which the
velocity is 4 m/s. The pressure is — 35 KPa at A. The 15 cm
pipe discharges into the air at C. To what height h above B
can the water be raised if B is 2 m above A and 25 KW is
delivered to the pump? Assume that the pump operates at
70% efficiency and the frictional loss between A and C is 3
J/N. See Fig. D.
11. Fig. E shows a siphon
discharging oil (sp. gr. 0.90). The
siphon is composed of 8 cm pipe
from A to B followed by 10 cm
pipe from B to C. The head losses
are: 1 to 2: 0.30 J/N; 2 to 3: 0.20
J/N and 8 to 4: 1.00.J/N.
Compute the discharge and
determine the pressures at points 2 and 3.
12. A pump draws water from
reservoir A and lifts it to reservoir
B. The head losses are: A to 1:
V12/2g and 2 to B; 20 V22/2g.
Compute the output power in
KW of the pump and the
pressure head at point 2 if the
discharge is 15 liters/s. See fig. F.
13. The 60 cm pipe conducts water from
reservoir A to a pressure turbine which is
discharging through another 60 cm pipe into
tailrace B. The head losses are: A to 1: 5
V2/2g; 2 to B; 0.20 V2 /2g. If the discharge is
0.70m3, what input power is being given up
by the water to the turbine? Fig. G.
14. A fire pump delivers water through 15 cm main pipe to a hydrant to which is connected an
8 cm hose, terminating in a nozzle 2cm in diameter. The nozzle, trained vertically up, is 1.60 m
above the hydrant and 12m above the pump. The head losses are: Pump to hydrant: 3 J/N;
Hydrant: 2 J/N; hydrant to nozzle base: 12 J/N; Nozzle: 6% velocity head in the nozzle. If the
gage pressure at the pump is 550 KPa to what vertical height can the jet be thrown? Neglect air
friction.
15. Water from a reservoir is pumped over a hill through a pipe 90 cm in diameter, and a
pressure of 200 KPa is maintained at the summit where the pipe is 90 m above the reservoir.
The quantity pumped is 1.40 m3/s and by reason of friction there is a head loss of 3 J/N
between reservoir and summit. If the pump is 90% efficient, determine the input power
furnished to the water.
16. The turbine shown in Fig. H:
extracts 50 J/N of water from
the given pipe system. At the
summit S 480. KPa is
maintained. Determine the flow
and the pressure at the
discharge side of the turbine
considering the following losses:
Summii to turbine: 4 times the
velocity head in the 20 cm pipe; Turbine to reservoir: 3 times the velocity head in the 30 cm
pipe.
17. A horizontal Venturi meter 45 cm by 60 cm is used to measure the flow of air through a 60
cm pipeline. A differential gage connected to the inlet and the throat contains water which is
deflected 10 cm. Considering the specific weight of air as 12.60 N/m3, find the flow of air.
neglect head losses.
18. A Venturi meter 60cm by 30 cm has its axis inclined downward 30 deg from the horizontal.
The distance, measured along the axis, from the inlet to the throat is 1.20 m. The differential
manometer shows a deflection of 15 cm of mercury. If the flowing fluid is water, find the
discharge if C= 0.98.
19. A 6 cm fire hose discharges water through a nozzle having a diameter of 2.5 cm. The head
lost in the nozzle is 4% of the velocity head in the jet. If the gage pressure at the base of the
nozzle is 400 KPa, find the flow and the maximum horizontal range to which the stream can be
thrown.
20. Water is flowing through
the pipe system of Fig. I.
Calculate the power of the
turbine, neglecting losses.
21. Calculate the minimum power
of the pump which will send the
jet over the wall shown in Fig. J.
Neglect losses.
22. In Fig. K h, = 20 cm and h, = 30 cm. If
water is flowing, calculate the power of the
pump.
23. A 20 cm pipe contains a short section in which the diameter is gradually reduced to 7.5 cm
and then gradually enlarged to full size. The pressure of water at a point where the reduction
starts is 520 KPa. If the rate of flow is 35 liters/s, determine the pressure at the 7.5 cm section,
Neglect losses.
24. The inlet end of a pipe is 2.50 m above the discharge end. To maintain a flow of 35 liters/s
through the 15 cm pipe a pressure of 250 KPa at the inlet end is kept. Compute the head loss
while passing through the pipe and determine the energy per second it represents. Consider
water flowing.
25. A water motor is supplied from a horizontal 30 cm pipe and uses 220 liters/s. Discharge
takes place through a 60 cm vertical pipe. A differential gage tapped into the pipe close to the
motor shows a deflection of 1.80 m of mercury. The two points where the gage was tapped are
separated by a vertical distance of 1 m. If the motor is 80% efficient, determine its Power
output.
26. A pump draws water from a pit through a vertical 30 cm pipe which extends below the
water surface. It discharges into a 15 cm horizontal pipe 4.0 m above the water surface. While
pumping 60 liters/s, a pressure gage on the discharge pipe reads 165 KPa and a gage on the
suction pipe shows a vacuum of 35 Kpa. Both gages are close to the pump and are separated
by a vertical distance of 90.cm. Compute the head lost in the suction pipe. Compute the
change in energy per second between the gages. What is the power output of the pump?
27. A free jet of water 5 cm in diameter is discharged from a nozzle at an angle of 60 deg. from
the horizontal. If the pressure at the 10 cm base, 30 cm from the tip, is maintained at 465 KPa
and Cv = 0.97, what is the maximum distance that the nozzle can be placed from a building and
still get water into a window which is 20 m above the nozzle?
28. A Pitot tube in a pipe in which
air is flowing is connected to a
manometer containing water as in
Fig. L. If the difference in water
levels in the manometer is 10 cm,
what is the velocity of flow in the
pipe? Assume a tube coefficient of
Cp = 0.99. Specific weight of air is
12 N/m3.
29. In Fig. M is shown a vertical pipe discharging water from an
elevated tank into the atmosphere. If the pipe is 15 cm in diameter
and the head loss is 0.04 v2/2g J/N per meter of pipe, compute the
discharge and the pressure head, in the pipe 30 cm below point A.
30. In Fig. N 85 liters/s of water enter through the 12 diameter
pipe at A and discharges radially in all directions between the
circular plates 60 cm in diameter and 2.50 cm apart,
discharging into the air. Neglecting friction, determine the
absolute pressure at point B.