Port-Said University
Faculty of Engineering Fluid Mechanics
Mech. Power Eng. Dept. Sheet No. (3)
1- Water flows steadily through a closed tank, as in Fig. (1). At section 1, D1 = 6 cm
and the volume flow is 100 m3/h. At section 2, D2 = 5 cm and the average velocity is
8 m/s. If D3 = 4 cm, what is (a) Q3 in m3/h and (b) average V3 in m/s?
2- In Fig. (2) the fluid is gasoline (SG = 0.68) at a mass flow rate of 12 kg/s.
Assuming no losses, estimate the gage pressure at section 1.
3- An incompressible liquid flows steadily along the pipe shown in Fig. (3). Determine
the direction of flow and the head loss over the 6-m length of pipe.
4- A flow of water is steadily discharged through a frictionless nozzle, Fig. (4). Find
the relation between the discharge velocity (v2) and the tank free surface height (h).
5- The siphon in Fig. (5) will run continuously as long as reservoir fluid is available.
Show (a) that the exit velocity V2 depends only upon gravity and the distance H and
(b) that the lowest (vacuum) pressure occurs at point 3 and depends on the distance
L + H.
6- Water flows from a pressurized tank, through a 15-cm-diameter pipe, exits from a 5-
cm-diameter nozzle, and rises 6 m above the nozzle as shown in Fig. (6). Determine
the pressure in the tank if the flow is steady, frictionless, and incompressible.
7- A circular tank of diameter 4 m contains water up to a height of 5 m. The tank is
provided with an orifice of diameter 0.5 m at the bottom. Find the time taken by
water (i) to fall from 5 m to 2 m (ii) for completely emptying to tank. Take C d = 0.6
8- A horizontal boiler shell (i.e. a horizontal cylinder, Fig. 7) 2m diameter and 10m
long is half full of water. Find the time of emptying the shell through a short vertical
pipe, diameter 0.08m, attached to the bottom of the shell. Take the coefficient of
discharge to be 0.8.
9- A Venturi meter has a pipe diameter of 0.3 m and a throat diameter of 0.2 m.
Assuming the specific weight of the gas is 19.62 N/m3, calculate the discharge of the
flow when the pressure difference between the entrance and the throat is measured
as 0.06 m on a water U-tube manometer. (Cd = 0.96)
10- An orifice-meter with orifice diameter 10 cm is inserted in a pipe of 20 cm
diameter. The pressure gauge fitted upstream and downstream of the orifice meter
gives readings of 19.62 N/cm2 and 9.81 N/cm2 respectively. Coefficient of discharge
for the meter is given as 0.6. Find the discharge of water through pipe.
11- Determine the flow rate, Q, through the pipe in Fig. (8)
,12- Water flows through the pipe contraction shown in Fig. (9). For the given 0.2-m
difference in manometer level, determine the flow-rate as a function of the diameter
of the small pipe, D, for Figs. (9a and 9b).
13- A sharp crested rectangular weir is to be constructed across a stream in which the
normal flow is 200 L/s. If the maximum flow likely to occur in the stream is 5 times
the normal flow then determine the length of weir necessary to the limit the rise in
water level to 38.4 cm above that for normal flow. (Cd = 0.61)
14- A channel conveys 300 L/s of water, at the outlet end there is a 90o V-notch weir for
which the coefficient of discharge is 0.58. At what distance above the bottom of the
channel should the weir be placed in order to make the depth in the channel 1.3 m?
15- A 7.5-cm-diameter horizontal jet of water strikes a flat plate as indicated in Fig.
(10). Determine the jet velocity if a 45-N horizontal force is required to (a) hold the
plate stationary, (b) allow the plate to move at a constant speed of 3 m/s to the right.
16- A horizontal circular jet of air strikes a stationary flat plate as indicated in Fig. (11).
The jet velocity is 40 m/s and the jet diameter is 30 mm. If the air velocity
magnitude remains constant as the air flows over the plate surface in the directions
shown, determine: (a) the magnitude of FA, the anchoring force required to hold the
plate stationary; (b) the fraction of mass flow along the plate surface in each of the
two directions shown; (c) the magnitude of FA, the anchoring force required to allow
the plate to move to the right at a constant speed of 10 m/s.
17- The horizontal nozzle in Fig. (12) has D1 = 30 cm and D2 = 15 cm, with inlet
pressure p1 = 160 kPa. and u2 = 17 m/s. Compute the horizontal force provided by
the flange bolts to hold the nozzle fixed.
18- In a 45o bend a rectangular air duct of 1 m2 cross-sectional area is gradually reduced
to 0.5 m2 area (Fig. 13). Find the magnitude and direction of the force required to
the duct in position if the velocity at inlet 10 m/s, and pressure is 30 kPa.
19- A 250 L/s of water is flowing in a pipe having a diameter of 30 cm. If the pipe is
bend by 135o (Fig. 14). Find the magnitude and direction of the resultant force on
the bend. The pressure of water flowing is 390 kPa.
20- The horizontal lawn sprinkler in Fig. (15) has a water flow rate of 15 L/min
introduced vertically through the center. Estimate (a) the retarding torque required to
keep the arms from rotating and (b) the rotation rate (r/min) if there is no retarding
torque.
21- A 0.5 L/s of water enter the rotor shown in Fig. (16) along the axis of rotation. The
cross-sectional area of each of the three nozzle exits normal to the relative velocity
is 18 mm2. How large is the resisting torque required to hold the rotor stationary?
How fast will the rotor spin steadily if the resisting torque is reduced to zero and (a)
θ = 0°, (b) θ = 30°, (c) θ = 60°, θ = 90o?
,22- Figure (17) shows a schematic of a centrifugal pump. Suppose r1 = 0.2 m, r2 = 0.5
m, and b = 0.15 m. Let the pump rotate at 600 r/min and deliver water at 2.5 m 3/s.
Determine the inlet and outlet of normal and tangent velocities. Compute the
idealized torque and power supplied.
Fig. (1) Fig. (2)
Fig. (3) Fig. (4)
6m
5 cm
0.6 m
15 cm
Fig. (5)
Fig. (6)
10 m
Fig. (7) Fig. (8)
, 6m
(a)
Fig. (10)
(b)
Fig. (9)
Fig. (12)
Fig. (11) Fig. (14)
6.5 mm
15 cm
Fig. (13) Fig. (15)
0.5
Fig. (16) Fig. (17)
Faculty of Engineering Fluid Mechanics
Mech. Power Eng. Dept. Sheet No. (3)
1- Water flows steadily through a closed tank, as in Fig. (1). At section 1, D1 = 6 cm
and the volume flow is 100 m3/h. At section 2, D2 = 5 cm and the average velocity is
8 m/s. If D3 = 4 cm, what is (a) Q3 in m3/h and (b) average V3 in m/s?
2- In Fig. (2) the fluid is gasoline (SG = 0.68) at a mass flow rate of 12 kg/s.
Assuming no losses, estimate the gage pressure at section 1.
3- An incompressible liquid flows steadily along the pipe shown in Fig. (3). Determine
the direction of flow and the head loss over the 6-m length of pipe.
4- A flow of water is steadily discharged through a frictionless nozzle, Fig. (4). Find
the relation between the discharge velocity (v2) and the tank free surface height (h).
5- The siphon in Fig. (5) will run continuously as long as reservoir fluid is available.
Show (a) that the exit velocity V2 depends only upon gravity and the distance H and
(b) that the lowest (vacuum) pressure occurs at point 3 and depends on the distance
L + H.
6- Water flows from a pressurized tank, through a 15-cm-diameter pipe, exits from a 5-
cm-diameter nozzle, and rises 6 m above the nozzle as shown in Fig. (6). Determine
the pressure in the tank if the flow is steady, frictionless, and incompressible.
7- A circular tank of diameter 4 m contains water up to a height of 5 m. The tank is
provided with an orifice of diameter 0.5 m at the bottom. Find the time taken by
water (i) to fall from 5 m to 2 m (ii) for completely emptying to tank. Take C d = 0.6
8- A horizontal boiler shell (i.e. a horizontal cylinder, Fig. 7) 2m diameter and 10m
long is half full of water. Find the time of emptying the shell through a short vertical
pipe, diameter 0.08m, attached to the bottom of the shell. Take the coefficient of
discharge to be 0.8.
9- A Venturi meter has a pipe diameter of 0.3 m and a throat diameter of 0.2 m.
Assuming the specific weight of the gas is 19.62 N/m3, calculate the discharge of the
flow when the pressure difference between the entrance and the throat is measured
as 0.06 m on a water U-tube manometer. (Cd = 0.96)
10- An orifice-meter with orifice diameter 10 cm is inserted in a pipe of 20 cm
diameter. The pressure gauge fitted upstream and downstream of the orifice meter
gives readings of 19.62 N/cm2 and 9.81 N/cm2 respectively. Coefficient of discharge
for the meter is given as 0.6. Find the discharge of water through pipe.
11- Determine the flow rate, Q, through the pipe in Fig. (8)
,12- Water flows through the pipe contraction shown in Fig. (9). For the given 0.2-m
difference in manometer level, determine the flow-rate as a function of the diameter
of the small pipe, D, for Figs. (9a and 9b).
13- A sharp crested rectangular weir is to be constructed across a stream in which the
normal flow is 200 L/s. If the maximum flow likely to occur in the stream is 5 times
the normal flow then determine the length of weir necessary to the limit the rise in
water level to 38.4 cm above that for normal flow. (Cd = 0.61)
14- A channel conveys 300 L/s of water, at the outlet end there is a 90o V-notch weir for
which the coefficient of discharge is 0.58. At what distance above the bottom of the
channel should the weir be placed in order to make the depth in the channel 1.3 m?
15- A 7.5-cm-diameter horizontal jet of water strikes a flat plate as indicated in Fig.
(10). Determine the jet velocity if a 45-N horizontal force is required to (a) hold the
plate stationary, (b) allow the plate to move at a constant speed of 3 m/s to the right.
16- A horizontal circular jet of air strikes a stationary flat plate as indicated in Fig. (11).
The jet velocity is 40 m/s and the jet diameter is 30 mm. If the air velocity
magnitude remains constant as the air flows over the plate surface in the directions
shown, determine: (a) the magnitude of FA, the anchoring force required to hold the
plate stationary; (b) the fraction of mass flow along the plate surface in each of the
two directions shown; (c) the magnitude of FA, the anchoring force required to allow
the plate to move to the right at a constant speed of 10 m/s.
17- The horizontal nozzle in Fig. (12) has D1 = 30 cm and D2 = 15 cm, with inlet
pressure p1 = 160 kPa. and u2 = 17 m/s. Compute the horizontal force provided by
the flange bolts to hold the nozzle fixed.
18- In a 45o bend a rectangular air duct of 1 m2 cross-sectional area is gradually reduced
to 0.5 m2 area (Fig. 13). Find the magnitude and direction of the force required to
the duct in position if the velocity at inlet 10 m/s, and pressure is 30 kPa.
19- A 250 L/s of water is flowing in a pipe having a diameter of 30 cm. If the pipe is
bend by 135o (Fig. 14). Find the magnitude and direction of the resultant force on
the bend. The pressure of water flowing is 390 kPa.
20- The horizontal lawn sprinkler in Fig. (15) has a water flow rate of 15 L/min
introduced vertically through the center. Estimate (a) the retarding torque required to
keep the arms from rotating and (b) the rotation rate (r/min) if there is no retarding
torque.
21- A 0.5 L/s of water enter the rotor shown in Fig. (16) along the axis of rotation. The
cross-sectional area of each of the three nozzle exits normal to the relative velocity
is 18 mm2. How large is the resisting torque required to hold the rotor stationary?
How fast will the rotor spin steadily if the resisting torque is reduced to zero and (a)
θ = 0°, (b) θ = 30°, (c) θ = 60°, θ = 90o?
,22- Figure (17) shows a schematic of a centrifugal pump. Suppose r1 = 0.2 m, r2 = 0.5
m, and b = 0.15 m. Let the pump rotate at 600 r/min and deliver water at 2.5 m 3/s.
Determine the inlet and outlet of normal and tangent velocities. Compute the
idealized torque and power supplied.
Fig. (1) Fig. (2)
Fig. (3) Fig. (4)
6m
5 cm
0.6 m
15 cm
Fig. (5)
Fig. (6)
10 m
Fig. (7) Fig. (8)
, 6m
(a)
Fig. (10)
(b)
Fig. (9)
Fig. (12)
Fig. (11) Fig. (14)
6.5 mm
15 cm
Fig. (13) Fig. (15)
0.5
Fig. (16) Fig. (17)
