JNTU
JNTU B.Tech II Year HYDRAULICS AND HYDRAULIC MACHINERY Previous Question Paper (March - 2022 - R15)
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Main
Derive the equation for specific energy curve.
Answer
Specific energy (E) is defined as the energy per unit weight of water measured with respect to the channel bed as the datum. For a rectangular channel with flow depth y and mean velocity v, the total energy head is given by E = y + (v2 / 2g). Since the discharge per unit width q = v * y, the velocity can be expressed as v = q / y. Substituting this into the energy equation yields the specific energy equation:
To derive the curve, we plot E on the x-axis and y on the y-axis. The equation represents a cubic curve with two limbs: one asymptotic to the line E = y (representing high-velocity, low-depth supercritical flow) and the other asymptotic to the y-axis (representing low-velocity, high-depth subcritical flow). The minimum specific energy occurs at the critical depth (yc), found by setting dE/dy = 0, which results in yc = (q2 / g)1/3.
Determine approximate water surface slope (m per km) at a point in a rectangular channel in which the discharge is 0.84 m3/s, the bed width is 3 m, the depth of flow is 0.75 m and the bed slope is 0.15 m per km. Assume C in Chezy’s formula as 55 and take energy coefficient alpha equal to unity.
Answer
Given: Discharge Q = 0.84 m3/s, width B = 3 m, depth y = 0.75 m, bed slope S0 = 0.15/1000 = 0.00015, Chezy constant C = 55, and energy coefficient α = 1. The cross-sectional area A = B * y = 3 * 0.75 = 2.25 m2. The wetted perimeter P = B + 2y = 3 + 2(0.75) = 4.5 m. The hydraulic radius R = A / P = 2.25 / 4.5 = 0.5 m.
The velocity v = Q / A = 0.84 / 2.25 = 0.3733 m/s. Using Chezy's formula v = C(RSf)1/2, we solve for the friction slope Sf:
The water surface slope Sw is given by the relation Sw = S0 - (d/dx)(v2/2g) - Sf. Assuming uniform flow conditions or a long channel reach where the velocity head change is negligible, Sw ≈ S0 - Sf = 0.00015 - 0.000092 = 0.000058. Converting to meters per kilometer, the slope is 0.058 m/km.
Derive the dynamic equation for steady gradually varied flow in an open channel.
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Explain the distinction between Rayleigh’s method and Buckingham's method of dimensional analysis.
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Using Buckingham’s theorem, prove that the discharge formula of a triangular notch is given by Q = H2 φ [ θ, μ / ρ g0.5 H2.5 ], where H = head over the notch, ρ = fluid density, μ = fluid viscosity, θ = notch angle, g = gravitational acceleration and φ = a functional notation.
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Using Rayleigh's method establish the following functional relation for the resisting torque T of a journal bearing: T = μ N D3 φ ( μ N / p ), where D = diameter of shaft, N = rpm of shaft, p= bearing pressure on lubricant, μ = viscosity of lubricant and φ = functional notation.
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Explain the model and prototype relation requirements in dimensional analysis.
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Show that the force exerted by a jet of water on an inclined fixed plate in the direction of the jet is given by F = ρ a V2 sin2 θ. Where a = area of the jet, V = velocity of the jet, θ = inclination of the plate with the jet.
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A jet of water of diameter 50mm moving with a velocity of 20m/sec strikes a fixed plate in such a way that the angle between the jet and the plate is 60°. Find the force exerted by the jet on the plate i) In the direction normal to the plate, ii) In the direction of the jet.
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A jet of water of diameter 5 cm and velocity 20 m/s impinges on (a) a normal flat vane moving in the direction of jet at 7.6 m/s and (b) a series of normal flat vanes mounted on a wheel which has a tangential velocity of 7.5 m/s. Calculate force exerted, work done by water and efficiency of the system in both cases.
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Define specific speed of a hydraulic turbine. Derive an equation for specific speed in terms of operating speed, power and heads.
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Explain the factors involved in selection of a hydraulic turbine.
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Define centrifugal pump and explain the working procedure of a single-stage centrifugal pump with neat sketch.
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A centrifugal pump is to discharge 0.118 m3/s at a speed of 1450 rpm against head of 25 m. The impeller diameter is 250 mm, its width at outlet is 50 mm and manometer efficiency is 75%. Determine the vane angle at the outer periphery of the impeller.
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