JNTU
JNTU B.Tech II HYDRAULICS AND HYDRAULIC MACHINERY Previous Question Paper (November/December - 2020 - R15)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Find the bed slope of the trapezoid channel of bed width 6 m, depth of water 3 m and side of slope 3 horizontal to 4 vertical, when the discharge through the channel is 30 m3/s. Take Chezy’s constant C = 70.
Answer
To find the bed slope, we use the Chezy formula for discharge: Q = A × C × sqrt(m × i), where Q is discharge, A is cross-sectional area, C is Chezy's constant, m is hydraulic mean depth, and i is the bed slope.
Given parameters:
- Bed width (b) = 6 m
- Depth of water (y) = 3 m
- Side slope (n) = 3 horizontal to 4 vertical, so n = 3/4 = 0.75
- Discharge (Q) = 30 m3/s
- Chezy's constant (C) = 70
Step 1: Calculate the area of the trapezoidal section (A):
Step 2: Calculate the wetted perimeter (P):
Step 3: Calculate the hydraulic mean depth (m):
Step 4: Calculate the bed slope (i) using the Chezy formula:
The bed slope of the channel is 0.0001635.
Explain about hydraulic jump and energy dissipation for varied flow phenomena.
Answer
A hydraulic jump is a localized phenomenon occurring in open channel flow when liquid at high velocity discharges into a zone of lower velocity, resulting in a sudden rise in the liquid surface level. This transition represents a shift from supercritical flow (Froude number Fr > 1) to subcritical flow (Fr < 1), characterized by high turbulence, surface waves, and significant energy loss.
The energy dissipation occurs due to the formation of a turbulent roller where kinetic energy is converted into heat through eddy formation and internal friction. The energy loss (ΔE) in a hydraulic jump is given by the Belanger equation:
where y₁ and y₂ are the sequent depths before and after the jump, respectively. The efficiency of the jump is defined as the ratio of energy after the jump to the energy before the jump.
Key characteristics and applications include:
- Energy Dissipation: The jump acts as an effective energy dissipator at the toe of spillways and sluice gates, preventing downstream bed erosion and scouring by reducing the high kinetic energy of the discharge.
- Flow Measurement: It is used to increase the water level for irrigation distribution or to mix chemicals in water treatment processes.
- Stilling Basins: Engineers design stilling basins to force the hydraulic jump to occur within a controlled concrete structure, ensuring the energy is dissipated safely before the water enters the natural channel.
The magnitude of the jump and the resulting energy dissipation are directly proportional to the initial Froude number of the incoming flow. Higher Froude numbers lead to more intense turbulence and greater relative energy loss, which necessitates robust design of downstream protection works.
Derive an expression for the drag force on smooth sphere of diameter D, moving with a uniform velocity V in a fluid of density ρ and dynamic viscosity μ.
Answer
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A pipe of diameter 1.5 m is required to transfer an oil of sp.gr. 0.90 and viscosity 3 × 10-2 poise at the rate of 3000 litre/s. Tests were conducted on a 15 cm diameter pipe using water at 20° C. Find the velocity and rate of flow in the model. Viscosity of water at 20° C = 0.01 poise.
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A nozzle of 50 mm diameter delivers a stream of water at 20 m/s perpendicular to a plate that moves away from the jet at 5 m/s. Find the force on the plate, work done/sec, and the efficiency of the jet.
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Draw the layout of a typical hydropower installation and explain its components.
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A Kaplan turbine runner is to be designed to develop 9100 kW. The net available head is 5.6 m. If the speed ratio = 2.09, flow ratio = 0.68, overall efficiency = 86% and the diameter of the boss is 1/3 the diameter of the runner. Find the diameter of the runner, its speed and the specific speed of the turbine.
Answer
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A centrifugal pump rotating at 1000 r.p.m. delivers 160 litres/s of water against a head of 30 m. The pump is installed at a place where atmospheric pressure is 1 × 105 Pa (abs.) and vapour pressure of water is 3 kPa (abs.). The head loss in suction pipe is equivalent to 0.2 m of water. Calculate:
Minimum NPHS
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Maximum allowable height of the pump from free surface of water in sump.
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