The document contains a series of fluid mechanics problems involving calculations of dynamic and kinematic viscosities, flow rates, pressure drops, and head losses across various pipe systems and venturimeters. It includes details on specific gravity, dimensions of pistons, and pressure differentials with applications to real-world scenarios. Each problem is illustrated with figures and numerical values requiring analysis for viscous flow in different setups.

1. Question Bank
1. The space between two square flat parallel plates is filled with oil having a specific gravity of (0.95). Each
side of the plate is 60 cm. The thickness of the oil film is 12.5 mm. The upper plate, which moves at 2.5 m/s,
requires a force of 98.1N to maintain the speed, Determine:
(a) The dynamic viscosity of the oil in poise.
(b) The kinematic viscosity of the oil in stokes.
2. In the rectilinear chamber of Fig. (1), section 1 has a diameter of (4
in) and the flow in is (2cfs). Section 2 has a diameter of (3 in) and the
flow out is (36 fps) average velocity. Compute the average velocity
and volume flux at section 3 if (D3 = 1 in). Is the flow at 3 in or out?
Fig. (1)
3. In Figure (2), if PB-PA = 97.4 kPa, Calculate H.
Use: Sp.gr of Meriam red oil =0.827
Sp.gr of Mercury = 13.6
Fig. (2)
4. A pipe carrying oil of specific gravity (0.78), changes in
diameter from 200 mm diameter at a position A to 500 mm diameter at a position B which is 4 meters at a
higher level. If the pressures at A and B are 9.81 N/cm2
and 5.886 N/cm2
respectively and the discharge is 200
liters/s, determine the loss of head and direction of flow.
5. Prove that the resistance (F) of a sphere of diameter (d) moving at constant speed (u) through a fluid density
(ρ) and dynamic viscosity (µ) may be expressed as:
6. The diameters of a small piston and a large piston of a hydraulic jack are 3 cm and 10 cm respectively. A
force of 80 N is applied on the small piston. Find the load lifted by the large piston when:
(a) The pistons are at the same level.
(b) Small piston as 40 am above the large piston.
The density of the liquid in the jack is given as 1000 kg/m3
.

2. 7. Water flows through the horizontal branching pipe shown in the
figure, at a rate of 10 ft3
/s. If viscous effects are negligible,
determine the water speed at section (2), the pressure at section (3),
and the flowrate at section (4).
8. Given is a three-pipe series system, as in the bellow Figure, the
total pressure drop is PA - PB = 150,000 Pa, and the elevation drop
is ZA - ZB = 5 m. The pipe data are:
The fluid is water, ρ = 1000 kg/m3 and ν = 1.02 X 10-6 m2/s. Calculate the flow rate Q in m3
/h through the system.
9. A horizontal venturimeter with inlet diameter 20 cm and throat diameter 10 cm is used to measure the flow
of oil of (Sp. gr. 0.8). The discharge of oil through venturimeter is 60 liters/s. Find the reading of the oil-
mercury differential manometer. Take Cd = 0.98.
10. Water, ρ = 1.94 slugs/ft3
and ν = 0.000011 ft2
/s, is flowing between two reservoirs at 0.3
ft3
/s through 150 ft of 2-in-diameter pipe and several minor losses, as shown in the Fig. bellow.
The roughness ratio is Є/d = 0.001. Find the elevation Z2. (Use gravity= 32.2 ft/s2
).
11. The inlet and throat diameters of a horizontal venturimeter are 30 cm and 10 cm respectively.
The liquid flowing through the meter is water. The pressure intensity at inlet is 13.734 N/cm2
while the vacuum pressure head at the throat is 37 cm of mercury. Find the rate of flow. Assume
that 4% of the differential head is lost between the inlet and throat. Find Also the value of Cd
for the venturimeter.
12. A (15 cm) diameter vertical cylinder rotates concentrically inside another cylinder of diameter (15.10
cm). Both cylinders are (25 cm) high. The space between the cylinders is filled with a liquid whose viscosity
is unkown. If a torque of (12 Nm) is required to rotate the inner cylinder at (100) r.p.m., determine the
viscosity of the fluid.
Use: Surface area of cylinder (𝐴 = 𝜋D. L) , Torque= Force x D/2.

3. 13. In the shown system, pressure gage A reads (1.5 kPa) (gage). The fluids are at 20°C. Determine the
elevations z, in meters, of the liquid levels in the open Piezometer tubes B and C.
Additional Information:
At 20°C use the following specific weight (γ):
γair = 12 N/m3
γgasoline = 6670 N/m3
γGlycerin = 12360 N/m3
14. Differential manometer is connected at the two points A and B of two pipes as shown in Fig. 2. The
pipe A contains a liquid of (S.G. = 1.5) while pipe B contains a liquid of (S.G. = 0.9). The pressure at A
and B are (98 kPa) and (176.4 kPa) respectively. Find the difference in mercury level in the differential
manometer.
Fig. (2)
15. Three pipes of 400 mm, 200 mm and 300 mm diameters have lengths of (400 m, 200 m, and 300 m)
respectively. They are connected in series to make a compound pipe. The ends of this compound pipe
are connected with two tanks. If the total friction losses in the system are (16 m) of water and friction
factor (‘f) for these pipes is same and equal to (0.01). Determine the discharge through the compound
pipe neglecting the minor losses.
(20 Marks)
16. A pitot-tube is inserted in a pipe of (300 mm) diameter. The static pressure in pipe is (100 mm) of
mercury (vacuum). The stagnation pressure at the center of the pipe, recorded by the pitot-tube is
(0.981 N/cm2). Calculate the rate of flow of water through pipe, if the mean velocity of flow is (0.85)
times the central velocity. Take Cv= 0.98.
17. In the attached fig. (1), pipe A contains gasoline (S.G= 0.7),
pipe B contains oil (S.G= 0.9), and the manometer fluid is
mercury. Determine the new differential reading if the pressure
in pipe A is decreased (25 kPa), and the pressure in pipe B
remains constant. The initial differential reading is (0.3 m) as
shown.
Fig. (1)
18. Water flows through the horizontal branching pipe shown in
the fig. (2), at a rate of 10 ft3
/s. If viscous effects are negligible,
determine the water speed at section (2), the pressure at section
(3), and the flowrate at section (4).
Fig. (2)

4. 19. Determine the size of riveted steel pipe required to convey (1200 L/sec) of water for a distance
of (500 m) with a head loss of (50 m).
20. Derive the theoretical discharge equation for the shown venturemeter in fig. (3), consider a
venturimeter fitted in a horizontal pipe through which a fluid (water) is flowing.
Fig. (3)
21. Differential manometer is connected at the two points A and B of two pipes as shown in
(Fig.1). The pipe A contains a liquid of (S.G. = 1.5) while pipe B contains a liquid of (S.G. =
0.9). The pressure at A and B are (98 kPa) and (176.4 kPa) respectively. Find the difference in
mercury level in the differential manometer. Take (S.G. =13.6) for Mercury
Fig. (1)
22. In the rectilinear chamber of Fig. (2), section 1 has a
diameter of (4 in) and the flow in is (2cfs). Section 2 has a
diameter of (3 in) and the flow out is (36 fps) average
velocity. Compute the average velocity and volume flux at
section 3 if (D3 = 1 in). Is the flow at 3 in or out?
Fig. (2)
23. A pipe carrying oil of specific gravity (0.85), changes in diameter from 150 mm diameter at a
position A to 400 mm diameter at a position B which is 3 meters at a higher level. If the
pressures at A and B are 9.81 N/cm2
and 5.886 N/cm2
respectively and the discharge is (175)
liters/s, determine the loss of head and direction of flow.
24. A pitot-tube is inserted in a pipe of (300 mm) diameter. The static pressure in pipe is (100 mm)
of mercury (vacuum). The stagnation pressure at the center of the pipe, recorded by the pitot-tube
is (0.981 N/cm2
). Calculate the rate of flow of water through pipe, if the mean velocity of flow is
(0.85) times the central velocity. Take Cv= 0.98.
Take: g= 9.81 m/s2
, density of water =1000 kg/m3
, Sp.gr. of mercury =13.6