## Fluid Mechanics - 1 - Dec 2016

### Civil Engineering (Semester 3)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.

### Solve any four Q1 (a,b,c,d,e,f,g)

**1(a)** Explain surface tension and Capillarity(5 marks)
**1(b)** Define the terms Gauge pressure, Vacuum pressure and Absoulte Pressure. Indicate their relative positions on a chart.(5 marks)
**1(c)** Define the terms Stable, Unstable and Neutral Equilibrium with neat sketch.(5 marks)
**1(d)** Define the terms Source, Sink and Doublet.(5 marks)
**1(e)** Write the practical application of Bernoulli's Theorem.(5 marks)
**1(f)** Whatt is the difference between small orifice and large orifice? Explain the meaning and significance of Vena Contracta.(5 marks)
**1(g)** What is a Notch? How are the Notches classified?(5 marks)
**2(a)** The two large horiziontal plates of infinite extent are 2.5 cm apart and have liquid of viscosity 0.8Ns/m^{2} filled between them . What force is required to pull a thin plate of negligible thickness and area 0.5m^{2} between the two large plates at a speed of 0.5 m/s if a) The thin plate is in the middle of the two large plates. b) The thin plate is at a distance of 1.0cm from one of the large plates.(10 marks)
**2(b)** A traingular lamina of base and altitude equal to 3.2 m is submerged in water vertically. Determine the total pressure and centre of pressure when a) Base of lamina coincides with the free surface and b) apex of triangular lamina coincides with free surface.(10 marks)
**3(a)** A solid cylinder 10 cm diameter and 40 cm long is made of two materials. The bottom 1 cm is of material of specific gravity 6.5 and the portion above of specific gravity 0.6. Does the cylinder float vertically in water of mass density 1000kg/m^{3}?(10 marks)
**3(b)** In a two-dimesional incompressible flow, the fluid velocity components are given by u = x-4y and v =-y-4x Show that the velocity potential exists and determine its form. Find also stream function.(10 marks)
**4(a)** A 15 cm ×5 cm Venturimeter is provided in a vertical pipe carrying crude oil of sp . gr. The flow is in upward direction. The difference of elevation between the entrance and throat section of venturimeter is 25 cm. The difference in level between the two limbs of U-tube mercury manometer recordedis 20 cm. Calculate i) flow rate of oil ii) pressure different between the entrance and throat section Take C_{d} as 0.95.(10 marks)
**4(b)** A tank containing water up to a depth of 500 mm is moving vertically upward with a constant acceleration of 2.45 m/s^{2}. Find the force exerted by water on the side of the tank. Also calcualte the force on the side of the tank when the width of the tank is 2 m and i) Tank is moving vertically downward with constant acceleration of 2.45 m/s^{2} ii) Tank is not moving at all.(10 marks)
**5(a)** A convergent divergent mouthpiece is fitted to the side of a tank. The discharge through mouthpiece under a constant head of 1.5 m is 5 lit/sec. The head loss in the divergent portion o.1 times the kinetic head at outlet. Find the throat and exit diameters if separation pressure is 2.5 m and atmospheric pressure head = 10.3 m of water.(10 marks)
**5(b)** Derive an equation for discharge over a Rectangular and Triangular Notch.(10 marks)
**6(a)** Write a short note on Borda's Mouthpiece(5 marks)
**6(b)** Describe Cipolleti Weir(5 marks)
**6(c)** Explain experimental determination of Hydraulic Coefficients.(5 marks)
**6(d)** Derive equation for discharge over broad crested weir.(5 marks)