JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech II Year FLUID MECHANICS – II Previous Question Paper (March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
What do you understand by hydraulically efficient channel section? Derive an expression for hydraulically efficient trapezoidal channel section.
Answer
A hydraulically efficient channel section, also known as the most economical section, is one that provides the maximum discharge for a given cross-sectional area, roughness coefficient, and bed slope. For a fixed area, this is equivalent to minimizing the wetted perimeter (P), as the discharge (Q) is inversely proportional to the perimeter in Manning's or Chezy's equations.
For a trapezoidal section with area A, depth y, side slope 1:m (horizontal:vertical), and base width b:
Expressing b in terms of A: b = (A/y) - my. Substituting into P:
To minimize P, differentiate with respect to y and set to zero (dP/dy = 0):
Substituting A = by + my2:
This condition implies that the hydraulic radius R = A/P = y/2. Furthermore, the side slopes must be tangent to a semicircle inscribed in the channel cross-section.
Uniform flow occurs at a depth of 1.5 m in a long rectangular channel 3.0 m wide and laid at a slope of 0.0009. If Manning’s ‘n’ is 0.015, calculate the maximum height of the hump on the floor to produce critical depth and the width of contraction that will produce critical depth without increasing the upstream depth of flow.
Answer
Given: y1 = 1.5 m, B = 3.0 m, S0 = 0.0009, n = 0.015. First, calculate discharge Q using Manning's equation:
A = 3 × 1.5 = 4.5 m2; P = 3 + 2(1.5) = 6 m; R = 4.5/6 = 0.75 m.
Critical depth yc = (q2/g)1/3, where q = Q/B = 7.825/3 = 2.608 m2/s:
Specific energy E1 = y1 + v12/2g = 1.5 + (2.608/1.5)2 / (2 × 9.81) = 1.653 m. Specific energy at critical state Ec = 1.5 yc = 1.32 m. Max hump Δz = E1 - Ec = 1.653 - 1.32 = 0.333 m.
For contraction without changing upstream depth, E1 = Ec2 = 1.5 yc2. Thus yc2 = 1.653/1.5 = 1.102 m. Since yc2 = (q22/g)1/3, q2 = √(9.81 × 1.1023) = 3.65 m2/s. Contraction width Bc = Q/q2 = 7.825/3.65 ≈ 2.14 m.
Derive the dynamic equation of GVF.
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A hydraulic jump occurs in a V-shaped channel having sides sloping at 45°. If the depth of flow before and after the jump formation are 0.5 m and 1 m, determine the flow rate and Froude numbers before and after formation.
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State the Buckingham-Pi theorem and mention the advantages of dimensional analysis.
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The lift force (F_L) on the wing of an airfoil depends on the flow velocity (V), chord length (L), fluid density (ρ), fluid viscosity (µ), speed of the sound in the fluid (c) and angle of attack of the wing. Determine by dimensional analysis the Π-terms associated with the problem.
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What are distorted models? Give the advantages of distorted models.
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A pipe of diameter 1.5 m is required to transport an oil of specific gravity 0.9 and viscosity 0.003 poise at the rate of 3 m³/s. Tests were conducted on a 0.15 m diameter pipe using water. Find the velocity and rate of flow in the model. Assume viscosity of water as 0.01 poise.
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Show that the force exerted by a jet on a moving curved vane is greater than that on a moving flat plate.
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A metal plate of 10 mm thickness and 200 mm square is hung so that it can swing freely about the upper horizontal edge. A horizontal jet of water of 20 mm diameter impinges with its axis perpendicular and 50 mm below the edge of the hinge, and keeps it steadily inclined at 30° to the vertical. Find the velocity of the jet if the specific weight of the metal is 75.54 kN/m³.
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A jet of water having a velocity of 35 m/s impinges on a series of vanes moving with a velocity of 20 m/s. The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of 120°. Draw the triangles of velocities at inlet and outlet and find the angles of vanes tips so that water enters and leaves without shock, the work done per unit weight of water entering the vanes and the efficiency.
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Show that in the case of a Pelton wheel maximum hydraulic efficiency occurs when the bucket speed is half that of the velocity of the jet.
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An inward flow reaction turbine with radial discharge with an overall efficiency of 85% is required to develop 180 kW. The head is 10 m; peripheral velocity is 0.96√(2gh); radial velocity of flow is 0.36√(2gh). The wheel is to make 180 rpm. The hydraulic losses in the turbine are 25% of the available energy. Determine: (i) The angle of the guide blade at inlet. (ii) The wheel vane angle at inlet.
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A single acting reciprocating pump running at 30 r.p.m., delivers 0.012 m³/sec of water. The diameter of the piston is 25 cm and stroke length is 50 cm. Determine: (i) The theoretical discharge of the pump, (ii) Co-efficient of discharge and (iii) Slip and percentage slip of the pump.
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Explain the following: (i) Load factor (ii) Utilization factor (iii) Estimation of hydropower potential.
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