1.a. Calculate the capillary rise in a glass tube of 2.5 $\mathrm{mm}$ diameter when immersed vertically in (i) water and (ii) mercury. Take surface tension $\sigma=0.0725 \mathrm{N} / \mathrm{m}$ for water and $\sigma=0.50 \mathrm{N} / \mathrm{m}$ for mercury in contact with air. Take specific gravity of mercury as 13.6 and angle of contact $=128^{\circ} .$

1.b. Prove that the relationship between surface tension and pressure inside a droplet of liquid in excess of outside pressure is given by $\mathrm{p}=4 \sigma / \mathrm{d}$ .

1.c. A rectangular plate 0.50 $\mathrm{m} \times 0.50 \mathrm{m}$ dimensions having a weight 500 $\mathrm{N}$ slides down an inclined plane [Fig. $\mathrm{Ql}(\mathrm{c}) ]$ making $30^{\circ}$ angle with the horizontal at a velocity of 1.75 $\mathrm{m} / \mathrm{sec}$ . If the 2 $\mathrm{mm}$ gap between the plate and inclined surface is filled with a lubricating oil, find its viscosity.

2.a. State and prove Pascal's law.

2.b. Explain with neat sketch: ( i) Absolute pressure (ii) Vacuum pressure (iii) Gauge pressure

2.c. The right limb of a simple $U$ tube manometer containing mercury is open to the atmospheric, while the left limb is connected to a pipe in which a fluid of specific gravity 0.9 is flowing. The centre of the pipe is 12 $\mathrm{cm}$ below the level of mercury in the right limb. Find the pressure of fluid in the pipe if the difference of mercury level in the two limbs is 20 $\mathrm{cm} .$ \lt/div\gt \ltspan class='paper-ques-marks'\gt(3 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt **Module-2** \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt3.a. \lt/b\gt Show that centre of pressure lies below the centre of gravity in vertical plane surface submerged in liquid. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt3.b. \lt/b\gt A gate closing an opening is triangular in section as shown in Fig. $Q 3(b) .$ The gate is 1 $\mathrm{m}$ long (in the direction perpendicular to the plane of the paper) and it is made up of concrete weighing 24 $\mathrm{kN} / \mathrm{m}^{3}$ . If the gate is hinged at the top and freely supported at one of the bottom ends, find the height of water h on the upstream side when the gate will just be lifted. ![enter image description here][2] \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt OR \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt4.a. \lt/b\gt Derive continuity equation in 3 dimensional flow in Cartesian coordinates. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt4.b. \lt/b\gt The velocity components in a two dimensional flow field for an incompressible fluid are expressed as $U=y^{3} / 3+2 x-x^{2} y, V=x y^{2}-2 y-x^{3} / 3$ i) Show that these functions represent a possible case of fluid flow. ii) Obtain an expression for stream functions $\tau .$ \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt **Module-3** \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt5.a. \lt/b\gt State and derive modified Bernoulli's equation. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt5.b. \lt/b\gt A venture meter is to be fitted in a pipe 0.25 $\mathrm{m}$ diameter where the pressure head is 7.6 $\mathrm{mof}$ flowing liquid and the maximum flow is 8.1 $\mathrm{m}^{3}$ per minute. Find the least diameter of the throat to ensure that the pressure head does not become negative. Take $\mathrm{C}_{\mathrm{d}}=0.96$ . \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt OR \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt6.a. \lt/b\gt The water is flowing through a pipe having diameter of 20 $\mathrm{cm}$ and 10 $\mathrm{cm}$ at sections 1 and 2 respectively. The rate of flow through the pipe is 30 litres/sec. The section 1 is 3 $\mathrm{m}$ above datum and section 2 is 2 $\mathrm{m}$ above datum. If the pressure at section 1 is 25 $\mathrm{N} / \mathrm{cm}^{2}$ , find the intensity of pressure at section 2. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt6.b. \lt/b\gt A $45^{\circ}$ reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being 600 $\mathrm{mm}$ and 300 $\mathrm{mm}$ respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet to bend is 8.829 $\mathrm{N} / \mathrm{cm}^{2}$ and rate of flow of water is 600 lit/sec. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt **Module-4** \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt7.a.\lt/b\gt What are hydraulic coefficients of an orifice? Derive necessary expressions. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt7.b. \lt/b\gt For a Borda's mouthpiece (running free), show that the coefficient of contraction is $0.5 .$ OR \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt8.a. \lt/b\gt Derive the expression for discharge over a triangular notch. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt8.b. \lt/b\gt A Cipo letti weir of crest length 60 $\mathrm{cm}$ discharge water. The head of water over the weir is 360 $\mathrm{mm}$ . Find the discharge over the weir if the channel is 80 $\mathrm{cm}$ wide and 50 $\mathrm{cm}$ deep. Take $\mathrm{C}_{\mathrm{d}}=0.60 \mathrm{c}$ . \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt **Module-5** \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt9.a.\lt/b\gt Derive Dafey-Weisbach equation for head loss due to friction in a pipe. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt9.b. \lt/b\gt Three pipes of lengths $800 \mathrm{m}, 500 \mathrm{m}$ and 400 $\mathrm{m}$ and of diameters $500 \mathrm{mm}, 400 \mathrm{mm}$ and 300 $\mathrm{mm}$ respectively are connected in series. These pipes are to be replaced by a single pipe of length 1700 $\mathrm{m}$ . Find the diameter of the single pipe. \lt/div\gt \ltspan class='paper-ques-marks'\gt(5 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt9.c. \lt/b\gt Find the loss of head when a pipe of diameter 200 $\mathrm{mm}$ is suddenly enlarged to a diameter of 400 $\mathrm{mm}$ . the rate of flow of water through the pipe is 250 liters/s. \lt/div\gt \ltspan class='paper-ques-marks'\gt(3 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt OR \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt10.a. \lt/b\gt Explain water hammer. Derive the expression for water hammer due to sudden closure of valve and pipe is rigid. \lt/div\gt \ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt \ltspan class='paper-page-id'\gt00\lt/span\gt \lt/div\gt \ltDIV class='paper-question'\gt \ltDIV class='paper-ques-desc'\gt \ltb\gt10.b. \lt/b\gt A main pipe divides into two parallel pipes which again forms one pipe. The length and diameter for the first parallel pipe are 2000 $\mathrm{m}$ and 1.0 $\mathrm{m}$ respectively, while the length and diameter of $2^{\text { nd }}$ parallel pipe a000 $\mathrm{m}$ and 0.8 $\mathrm{m}$ . Find the rate of flow in each parallel pipe, if total flow in the main is 3.0 $\mathrm{m}^{3} / \mathrm{s}$ . The coefficient of friction for each parallel pipe is same and equal to 0.005.