JNTU
JNTU B.Tech II FLUID MECHANICS II Previous Question Paper (August/September – 2022 - R16)
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Main
Find the side slope in a trapezoidal section of maximum efficiency which will carry the same flow as a half square section of the same area.
Answer
For a trapezoidal channel of maximum efficiency, the hydraulic mean depth is half the depth of flow, R = y/2, and the side slope m is given by m = 1/√3. For a half-square section (a rectangular channel where b = 2y), the area is A = 2y2. For the trapezoidal section, A = (b + my)y. Equating the areas: (b + my)y = 2y2, which simplifies to b + my = 2y. Substituting the condition for maximum efficiency b + 2my = 2y√(1 + m2), we solve for m. Given the constraints, the side slope m for a most efficient trapezoidal section is 1/√3, which corresponds to an angle of 60° with the horizontal.
An open channel of trapezoidal section, 2.5 m at the base and having sides inclined at 60° to the horizontal, has a bed slope of 1 in 500. It is found that when the flow is 1.5 m3/s the depth of water in the channel is 0.5 m. Assuming the validity of the Manning‘s formula, calculate the flow when the depth is 0.7 m.
Answer
First, calculate the hydraulic properties for the given depths. For a trapezoidal section with base b = 2.5 m and side slope m = cot(60°) = 1/√3 ≈ 0.577: A = (b + my)y and P = b + 2y√(1 + m2). At y1 = 0.5 m: A1 = (2.5 + 0.577 × 0.5) × 0.5 = 1.394 m2; P1 = 2.5 + 2 × 0.5 × √(1 + 0.5772) = 3.655 m. R1 = A1/P1 = 0.381 m. Using Manning's formula Q = (1/n) A R2/3 S1/2, we find (1/n)S1/2 = Q1 / (A1 R12/3) = 1.5 / (1.394 × 0.3812/3) = 1.5 / 0.735 = 2.041.
At y2 = 0.7 m: A2 = (2.5 + 0.577 × 0.7) × 0.7 = 2.033 m2; P2 = 2.5 + 2 × 0.7 × 1.155 = 4.117 m. R2 = A2/P2 = 0.494 m. The new flow Q2 = (1/n)S1/2 × A2 × R22/3 = 2.041 × 2.033 × 0.4942/3 = 2.041 × 2.033 × 0.623 = 2.586 m3/s.
Explain how the hydraulic jump forms.
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A rectangular flume 2 m wide carries discharge at the rate of 2 m3/s. The bed slope of the flume is 0.0004. At a certain section the depth of flow is 1m. Calculate the distance of the section downstream where the depth of flow is 0.9m. Solve by using single step method. Assume rugosity coefficient as 0.014. Is the slope of the channel mild or steep? How is this type of profile classified? Normal depth yo = 1.082m.
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What is meant by geometric, kinematic and dynamic similarities? Are these similarities truly attainable? If not why?
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Define the following non-dimensional numbers: Reynold’s number, Froude’s number and Mach’s number. What are their significances for fluid flow problems?
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A 1:10 scale model of a submarine moving far below the surface of water is tested in a water tunnel. If the speed of the prototype is 8 m/s, determine the corresponding velocity of water in the tunnel. Also determine the ratio of the drag for the model and the prototype. νseawater = 1.121×10-6 m2/s, νwater = 1.00×10-6 m2/s, ρseawater = 1027 Kg/m3, ρwater = 1000kg/m3.
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Derive an expression for the force exerted by a jet of water on a moving plate held inclined to the direction of jet.
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A jet of water having a velocity of 20 m/s strikes a curved vane which is moving with a velocity of 9 m/s. The vane is symmetrical and is so shaped that the jet is deflected through 120°. Find the angle of the jet at inlet of the vane so that there is no shock. What is the absolute velocity of the jet at outlet in magnitude and direction and the work done per second per unit weight of water striking? Assume the vane to be smooth.
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Derive the expression for specific speed of a turbine.
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A Kaplan turbine is to develop 2400 KW when running at 240 rpm under a net head of 49m. In order to predict its performance a model of scale 1:5 is tested under a net head of 25m. At what speed should the model run and what power would it develop. Determine the discharge in the model and in full scale turbine if the overall efficiency of the model is 85%.
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Define cavitation, what are the effects of cavitation? Give the necessary precautions against cavitation.
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The diameter and width of a centrifugal pump impeller are 50 cm and 2.5 cm. The pump runs at 1200 rpm. The suction head is 6 m and the delivery head is 40m. The frictional drop in suction is 2 m and in the delivery 8 m. The blade angle at out let is 30°. The manometric efficiency is 80% and the overall efficiency is 75%. Determine the power required to drive the pump. Also calculate the pressures at the suction and delivery side of the pump.
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