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# Indian Institute of Technology Madras (IIT-M) 2007 B.Tech Civil Engineering Hydraulic Engineering,End sem - Question Paper

Wednesday, 23 January 2013 03:30Web

DEPARTMENT OF CIVIL ENGINEERING, I.I.T. MADRAS
CE-204: Hydraulic Engineering
Final exam
Date: 28-April-2007, Duration: three hours, Maximum Marks: 150

1. A gate of size two m X one m can slide without friction as shown. It is held in place by a thin cable which pulls it to the left due to buoyancy on a balloon of diameter D and of negligible weight. The gate just opens when the level of water is as shown. find D. Where should the cable be attached so that the gate slides smoothly (without rotation ) inside the channel? [Marks16]

2. A 300 reducing elbow is shown. The fluid is water. Evaluate the components of force that must be given by the adjacent pipes to keep the elbow from moving. The bend is in a horizontal plane. [Marks20]

3. An 8-m wide rectangular channel has a flow velocity and flow depth of four m/s and four m, respectively. The channel bottom is at El. 700 m. Assuming no losses, design a transition so that the water level downstream of the transition is at El. 703.54 m, if the channel width remains constant. [marks16]

4. The specific energy in a 2.0 m wide rectangular channel is not to exceed 1.2 m. What maximum discharge can be carried in such a channel? What longitudinal slope is needed to sustain such a flow? presume Manning roughness coefficient, n = 0.015. [Marks16]

5. A long and wide rectangular channel (n = 0.016) has a discharge intensity of 4.0 m3/s per meter width. If the bed slope modifications from 0.008 to 0.012 at a section, sketch the possible GVF profiles due to this break in grade. Also tag the water surface profiles. Detailed explanation should be provided for your ans. [marks16]

6. An agitator of diameter D requires power P to rotate at a constant speed N in a liquid of density ? and dynamic viscosity µ. Determine the non-dimensional parameters which define this process. An agitator 225 mm diameter rotating at 23 rev/s in water requires a driving torque of 1.1 N-m. compute the corresponding speed and the torque needed to drive a similar agitator of 675 mm diameter rotating in air. (Density of air = 1.20 Kg/m3, Dynamic viscosity of air = 1.86 x 10-5 Pa.s, Dynamic viscosity of water = 1.01 x 10-3 Pa.s) [Marks20]

7. Irrigation water is to be pumped through a steel pipe two km long and one m in diameter. From a river to an irrigation canal at a rate of 2.50 m3/s. The water surface elevation at the pump intake is 100 m and in the canal is 150 m. What power should be supplied to the pump if the pump efficiency is 82% and the inlet and outlet head losses are nil. The equivalent sand grain roughness height for steel is 4.6x10-2 mm. [Marks12]

8. Schematic of a water distribution network is shown beneath. Pipe lengths, diameters, friction factors, and the valve characteristics at every of the outlets are provided. Reservoir water level at time t = 0 as well as the reservoir cross sectional area is also provided. discuss the method (in detail) 1 needs to follow (along with the formulation of equations) to determine the water level variation in the reservoir with time. [Marks24]

9. [Marks12]
(i) Explain Prandtl’s mixing length theory for modeling turbulent viscosity.
(ii) Explain how you would create a hydraulic jump in a laboratory channel. 