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Centurion University of Technology and Management

Paralakhemundi

Fluid flow and Flow measurement

(For B.Tech III SemesterChemical Engineering)

Assignment-I

Short questions

1. Define pressure. Obtain an expression for the pressure intensity at a point in a fluid.2. What is the difference between dynamic viscosity and kinematic viscosity? What are their units of measurement?3. What is pitot tube? How will you determine the velocity at any pointwith the help of pitot tube?4. What are hydraulic coefficients? Name them.5. Define vena contracta?6. What is meant by intensity of pressure? How it varies with depth of fluid?7. What is the relation between vaccum and absolute preeure?8. What conditions lead to cavitation? Is cavitation possible in a free surface flow?9. What are the limitations of the bernoullis equation?10.What quantities are determined by

i. A pitot tube

ii. A venturimeter

iii. A piezometer

iv. A manometer

v. A combination of a piezometer and pitot tube11.What is the difference between the pitot tube and the pitot static tube?12.Define continuity equation and the bernoullis equation.13.What are the assumptions made in Bernoullis equation?14.How a rotatmeter is used for measuring flow rate?15.How to measure discharge through an open channel?

Long questions

1. A drop of liquid spreads over a horizontal surface. Obtain dimensionless groups of the variables which will influence the rate at which the liquid

spreads.

2. A glass particle settles under the action of gravity in a liquid. Obtain a dimensionless grouping of the variables involved. The falling velocity is found to

be proportional to the square of the particle diameter when the other variables are constant. What will be the effect of doubling the viscosity of the

liquid?

3. Two storage tanks, A and B, containing a petroleum product, discharge through pipes each 0.3 m in diameter and 1.5 km long to a junction at D, as

shown in Figure 3.9. FromD the liquid is passed through a 0.5 m diameter pipe to a third storage tankC, 0.75 km away. The surface of the liquid in A isinitially 10 m above that in Cand the liquid level inB is 6 rn higher than that inA. Calculate the initial rate of discharge of liquid into tankCassuming

the pipes are of mild steel. The density and viscosity of the liquid are 870 kg/m3 and 0.7 mN s/m2 respectively.

4. 98% sulphuric acid of viscosity 0.025 N s/m2 and density 1840 kg/m3 is pumped at 685cm3/s through a 25 mm line. Calculate the value of the Reynolds

number.

5. The power required by an agitator in a tank is a function of the following four variables:

(a) diameter of impeller,

(b) Number of rotations of the impeller per unit time,

(c) Viscosity of liquid,

(d) Density of liquid.

From a dimensional analysis, obtain a relation between the power and the four variables. The power consumption is found, experimentally, to be

proportional to the square of the speed of rotation. By what factor would the power be expected to increase if the impeller diameter were doubled?

6. The rate of discharge of water from a tank is measured by means of a notch, for which the flow rate is directly proportional to the height of liquid

above the bottom of the notch. Calculate and plot the profile of the notch if the flow rate is 0.1 m 3/s when the liquid level is 150 mm above the

bottom of the notch.7. The rate of flow of water in a 150 mm diameter pipe is measured by means of a venturi meter with a 50 mm diameter throat. When the drop in head

over the converging section is 100 mm of water, the flow rate is 2.7 kg/s. What is the coefficient for the converging cone of the meter at that flow

rate and what is the head lost due to friction? If the total loss of head over the meter is 15 mm water, what is the coefficient for the diverging cone?

8. A venturi meter with a 50 mm throat is used to measure a flow of slightly salt water in a pipe of inside diameter 100 mm. The meter is checked by

adding 20 cm3/s of normal sodium chloride solution above the meter and analysing a sample of water downstream from the meter. Before addition

of the salt, 1000 cm3 of water requires 10 cm3 of 0.1 M silver nitrate solution in a titration. 1000 cm3 of the downstream sample required 23.5 cm3

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of 0.1 M silver nitrate. If a mercury-under-water manometer connected to the meter gives a reading of 221 mm, what is the discharge coefficient ofthe meter? Assume that the density of the liquid is not appreciably affected by the salt.

9. Air at 323 K and 152 kN/m2 flows through a duct of circular cross-section, diameter 0.5 m. In order to measure the flowrate of air, the velocity

profile across a diameter of the duct is measured using a pitot-static tube connected to a water manometer inclined at an angle of cos_1 0.1 to the

vertical. The following results are obtained

Calculate the mass flowrate of air through the duct, the average velocity, the ratio of the average to the maximum velocity and the Reynolds number.

Comment on these results. Discuss the application of this method of measuring gas flowrates, with particular emphasis on the best distribution of

experimental points across the duct and on the accuracy of the results. Take the viscosity of air as 1.9 *10 -2mN s/m2 and the molecular weight of air as

29 kg/kmol.

10.Water (density 1000 kg/m3, viscosity 1 mNs/m2) is pumped through a 50 mm diameter pipeline at 4 kg/s and the pressure drop is 1 MN/m2. What

will be the pressure drop for a solution of glycerol in water (density 1050 kg/m3, viscosity 10 mNs/m2) when pumped at the same rate? Assume the

pipe to be smooth.

11.Water is flowing through a 100 mm diameter pipe and its flowrate is metered by means of a 50 mm diameter orifice across which the pressure drop

is 13.8 kN/m2

. A second stream, flowing through a 75 mm diameter pipe, is also metered using a 50 mm diameter orifice across which the pressuredifferential is 150 mm measured on a mercury-underwater manometer. The two streams join and flow through a 150 mm diameter pipe. What would

you expect the reading to be on a mercury-under-water manometer connected across a 75 mm diameter orifice plate inserted in this pipe? The

coefficients of discharge for all the orifice meters are equal. Density of mercury = 13600 kg/m3.

12.Water is flowing through a 150 mm diameter pipe and its flow rate is measured by means of a 50 mm diameter orifice, across which the pressure

differential is 2.27 x 104 N/m2. The coefficient of discharge of the orifice meter is independently checked by means of a pitot tube which, when

situated at the axis of the pipe, gave a reading of 100 mm on a mercury-under-water manometer. On the assumption that the flow in the pipe is

turbulent and that the velocity distribution over the cross-section is given by the Prandtl one-seventh power law, calculate the coefficient of

discharge of the orifice meter.