1.a. Distinguish between

i) Ideal fluid and real fluid

ii) Newtonion and non Newtonion fluid

ii) Cohesion and adhesion

1.b. State and prove Pascal's law.

1.c. Calculate the specific weight, density, specific volume and specific gravity of two litres of a liquid which weighs 15 $\mathrm{N}$ .

2.a. With the help of neat sketches, explain (i) simple U-tube manometer and (ii) differential U-tube manometer.

2.b. What is capillarity? Derive an expression for capillary rise and a liquid in a glass tube.

2.c. A $\mathrm{U}$ tube differential manometer connects two pipes $\mathrm{A}$ and $\mathrm{B}$ . Pipe A contains carbon tetra chloride having specific gravity 1.594 under a pressure of 117.72 $\mathrm{kN} / \mathrm{m}^{2}$ and pipe $\mathrm{B}$ contains oil of specific gravity 0.8 under a pressúre of 117.72 $\mathrm{kN} / \mathrm{m}^{2}$ . The pipe A lies 2.5 $\mathrm{m}$ above pipe $\mathrm{B}$ . Find the difference in pressure measured by mercury as fluid filling U-tube. Assume mercury in the right limb is 50 om below centre of pipe B.

3.a. Distinguish between:

i) Steady and unsteady flow

ii) Rotational, and irrotational flow

3.b. Derive the expressions for total pressure and centre of pressure for a plane surface submerged vertically in a liquid.

3.c. A circular opening 3 $\mathrm{m}$ diameter, in a vertical side of a tank is closed by a disc of 3 $\mathrm{m}$ diameter which can yotate about a horizontal diameter. Calculate: (i) The force on the disc, and (ii) The torque required to maintain the disc in equilibrium in vertical position when the head of water above the horizontal diameter is 6 $\mathrm{m}$ .

4.a. Define the terms velocity potential function and stream function.

4.b. Derive an expression for continuity equation for a three dimensional flow.

4.c. A stream function in a two dimensional flow is $\psi=2 \mathrm{xy}$ . Show the flow is irrotational and determine the corresponding velocity potential $\phi$ .

5.a. What is pitot tube? How will you determine velocity using pitot tube?

5.b. State and prove Bernoulli's theorem for steady flow of an incompressible fluid.

5.c. The water is flowing through a tapper pipe of length 100 $\mathrm{m}$ having diameters 600 $\mathrm{mm}$ at the upper end and 300 $\mathrm{mm}$ at the lower end at the rate of 50 litres/s. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher end is 196.2 $\mathrm{kPa}$.

6.a. Define the terms: i) forced vertex flow and ii) free vertex flow.

6.b. What is venturimeter? Derive an expression for discharge through a venturimeter.

6.c. A pipe of 300 $\mathrm{mm}$ diameter conveying 300 litres/s of water has a right angled bend in a horizontal plane. Find the resultant force exerted on the bend if the pressure at inlet and outlet of bend are 245.25 $\mathrm{kPa}$ and 235.44 $\mathrm{kPa}$ .

7.a. Explain different hydraulic coefficient and establish the relation between them.

7.b. Derive an expression for discharge over a triangular notch.

7.c. The head of water over an orifice of diameter 100 mm is 5 m. The water coming out from the orifice is collected in a circular tank of diameter 2 m. The rise of water level in circular tank is 450 mm in 30 seconds. Also the coordinates at a certain point on the jet, measured from vena-contracta are 100 mm horizontal and 52 mm vertical. Find the hydraulic coefficients $\mathrm{C}_{\mathrm{v}}, \mathrm{C}_{\mathrm{d}}$ and $\mathrm{C}_{\mathrm{C}}$.

8.a. Explain the terms:

i) Velocity of approach

ii) Effect of end contractions in notches

8.b. What is Cipolletti notch? Derive an expression for discharge over a Cipolletti notch.

8.c. Water flows over a rectangular weir 1$/ 2 \mathrm{m}$ wide at a depth of 15 $\mathrm{cm}$ and afterwards passes through a triangular right angled weir. Taking coefficient of discharge for rectangular Weir 0.62 and for triangular Weir 0.59 find the depth over the triangular Weir.

9.a. Explain briefly

i) Hydraulic gradient line and

ii) Energy gradient line

9.b. Derive an expression for head loss due to friction in pipes.

9.c. A rigid pipe conveying water is 3200 $\mathrm{m}$ long. The velocity of flow is 1.2 $\mathrm{m} / \mathrm{s}$ . Calculate the rise of pressure behind a valve at the lower end if it is closed (i) in 20 seconds (ii) in 3 sconds. Take bulk modulus and water equal to 2000 $\mathrm{N} / \mathrm{mm}^{2}$.

10.a. Explain briefly the phenomenon of water hammer.

10.b. Derive an expression for head loss due to sudden enlargement in a pipe flow.

10.c. At a sudden enlargement of a water main from 240 $\mathrm{mm}$ to 480 $\mathrm{mm}$ diameter, the hydraulic gradient rises by 10 $\mathrm{mm}$ . Estimate the rate of flow.