ESO204: FLUID MECHANICS AND RATE PROCESSES
Semester: 2024-25-I
Instructor: Arun K Saha
Practice Problems Set -1
Q1. Calculate the density, specific weight and weight of one liter of petrol of specific gravity =0.7.
Q2. For low-speed (laminar) flow in a tube of radius ro, the velocity u takes the form
where µ is viscosity and ∆p the pressure drop. What are the dimensions of B?
Q3. The velocity distribution for laminar flow between parallel plates is given by
Where h is the distance separating the plates and the origin is placed midway between the plates. Consider
a flow of water at 15ᵒC, with umax = 0.10 m/s and h = 0.25 mm. Calculate the shear stress on the upper
plate and give its direction. Sketch the variation of shear stress across the channel.
Q.4 In Fig.1, A hydraulic press has a ram of 30 cm diameter and a plunger of 4.5 cm diameter. Find the
weight lifted by the hydraulic press when the force applied at the plunger is 500N.
Fig. 1
Q5. The diameter of a small piston and a large piston of a hydraulic jack are 3cm and 10 cm respectively
as shown in Fig 2(a) and (b). A force of 80N is applied on the small piston. Find the load lifted by the
large piston when:
(a) The pistons are at same level.
(b) Small piston is 40 cm above the large piston.
The density of the liquid in jack is given as 1000 kg/m3.
Fig 2(a)
Fig 2(b)
Q6. The pressure intensity at a point in a fluid is given 3.924 N/cm2. Find the corresponding height of
fluid when the fluid is: (i) water and (ii) oil of sp. gr. 0.9.
Q7. What are the gauge pressure and absolute pressure at a point 3m below the free surface of a liquid
having density of 1530 kg/m3 if the atmospheric pressure is equivalent to 750mm of mercury? The
specific gravity of mercury is 13.6 and the density of water = 1000 kg/m3.
Q8. A U-Tube manometer is used to measure the pressure of water in pipeline. The contact between
water and mercury is in the left limb. Determine the pressure of water in the main line, if the difference
in the level of mercury in the limb of U-tube is 10 cm and the free surface of the mercury is in the level
with the centre of the pipe as shown in Fig. 3. If the pressure of water in pipe is reduced to 9810 N/m2,
calculate the new difference in the level of mercury. Sketch the arrangement for second case.
Fig. 3
Q9. Determine the gage pressure in kPa at point a, if liquid A has SG = 1.20 and liquid B has SG = 0.75.
The liquid surrounding point a is water, and the tank on the left is open to the atmosphere.
Fig.4
Q10. In Fig.5 all fluids are at 20ᵒC. Determine the pressure difference (Pa) between points A and B.
Fig.5
Q11. Water flows downward in a pipe at 45ᵒ, as shown in Fig.6. The pressure drop (P1 -P2) is partly due
to gravity and partly due to friction. The mercury manometer reads a 15.25 cm height difference. What
is the total pressure drop P1 -P2? What is the pressure drop due to friction only between 1 and 2?
Fig.6
Q12. In Fig.7 the pressures at A and B are the same, 100 kPa. If water is introduced at A to increase PAto
130 kPa, find and sketch the new positions of the mercury menisci. The connecting tube is a uniform 1cm diameter. Assume no change in the liquid densities.
Fig.7
Q13. A single column manometer is connected to a pipe containing a liquid of sp. gr. 0.9 as shown in
Fig. 8. Find the pressure in the pipe if the area of the reservoir is 100 times the area of the tube for the
manometer reading shown. The specific gravity of mercury is 13.6.
Fig. 8
Q14. Find out the differential reading ‘h’ of an inverted U-tube manometer containing oil of specific
gravity 0.7 as the manometric fluid when connected across pipes A and B as shown in Fig 9, Conveying
liquids of specific gravity 1.2 and 1.0 and immiscible with manometric fluid. Pipe A and Pipe B are
located at the same level and assumed the pressure at A and B to be equal.
Fig. 9
Q15. Gate AB in Fig.10 is 1.2 m long and 0.8 m into the paper. Neglecting atmospheric pressure,
compute the force F on the gate and its center-of-pressure position X.
Fig.10
Q16. Gate AB in Fig.11 is a homogeneous mass of 180 kg, 1.2 m wide into the paper, hinged at A, and
resting on a smooth bottom at B. All fluids are at 20ᵒC. For what water depth h will the force at point B
be zero?
Fig.11
Q17.The tank in Fig. 12 has a 4-cm-diameter plug at the bottom on the right. All fluids are at 20ᵒC. The
plug will pop out if the hydrostatic force on it is 25 N. For this condition, what will be the reading h on
the mercury manometer on the left side?
Fig.12
Q18. The dam in Fig.13 is a quarter circle 50 m wide into the paper. Determine the horizontal and vertical
components of the hydrostatic force against the dam and the point CP where the resultant strikes the dam.
Fig.13
Q19. The gate shown below (Fig. 14) is hinged at H. The gate is 3 m wide normal to the plane of the
diagram. Calculate the force required at A to hold the gate closed
Fig.14
Q20. Consider the cylindrical weir of diameter 3 m and length 6 m (Fig. 15). If the fluid on the left has
a specific gravity of 1.6, and on the right has a specific gravity of 0.8, find the magnitude and direction
of the resultant force.
Fig. 15