JNTU
JNTU B.Tech II FLUID MECHANICS Previous Question Paper (March - 2022 - R15)
Answer any five questions. All questions carry equal marks.
Main
State and explain the Newton‘s law of viscosity. Deduce the expression for the dynamic viscosity.
Answer
Newton's law of viscosity states that the shear stress on a fluid element is directly proportional to the rate of shear strain or the velocity gradient in the direction perpendicular to the plate. Mathematically, this is expressed as:
Where τ is the shear stress, μ is the dynamic viscosity (or coefficient of viscosity), and du/dy is the velocity gradient. For a fluid flowing between two parallel plates, where one plate is stationary and the other moves at velocity u at a distance y, the velocity gradient is assumed to be linear, u/y. The dynamic viscosity μ is derived by rearranging the expression as:
The unit of dynamic viscosity is N·s/m² or Pa·s.
A thin flat plate is dragged at a constant velocity of 7 m/s on the top of a 5 mm deep liquid layer of viscosity 25 centipoise. If the area of the plate is 1.5 m2. Find the drag force. Assume variation of velocity in the liquid to be linear.
Answer
Given data:
- Velocity (u) = 7 m/s
- Gap thickness (y) = 5 mm = 0.005 m
- Viscosity (μ) = 25 centipoise = 0.25 poise = 0.025 N·s/m²
- Area (A) = 1.5 m²
Since the velocity variation is linear, the velocity gradient is:
The shear stress (τ) is calculated as:
The drag force (F) is the product of shear stress and area:
The drag force required to move the plate is 52.5 N.
Explain with sketches, how an inverted U-tube manometer is used to measure small pressure differences.
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A rectangular plane surface 3 m wide and 4 m deep lies in water in such a way that its plane making an angle of 350 with the surface of water. Determine the total pressure force and position of center of pressure, when upper edge is 2m below the free surface.
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Distinguish between: (i) Steady flow and un-steady flow, (ii) Rotational and irrotational flow (iii) Laminar and turbulent flow.
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The velocity potential function for a two-dimensional flow is φ = x(2y-1) at a point P(4,5). Determine: i) The velocity and ii) The value of stream function.
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Define the following: i) Path line ii) Streak line iii) Stream lines iv) Stream tube.
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Define stream function and velocity potential function. Show that the lines of constant stream function and velocity potential function must intersect orthogonally.
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Find an expression for the discharge over a triangular notch in terms of head of water over the crest of the notch?
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Water flows at the rate of 0.147 m3/s through a 150 mm diameter orifice inserted in a 300mm diameter pipe. The pressure gauges fitted upstream and downstream of the orifice plate have shown the readings of 176.58 kN/m2 and 88.29 kN/m2 respectively, find the coefficient of discharge C of the orifice meter?
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Derive Bernoulli’s equation from fundamentals and write its limitations.
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A pipe of 310 mm diameter conveying 0.25 m3/s of water has a right-angled bend in a horizontal plane. Find the resultant force exerted on the bend if the pressure at inlet and outlet of the bend are 25.145 N/cm2 and 22.023 N/cm2.
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Explain boundary layer separation? Mention few methods to prevent or delay the separation of boundary layer?
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A thin plate is moving in still atmospheric air at a velocity of 4 m/s. The length of plate is 0.5 m and width is 0.34 m, calculate the thickness of boundary layer at the end of the plate and the drag force on one side of the plate. Take density of air is 1.25 kg/m3 and kinematic viscosity 0.15 stokes.
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Derive the equations for head loss in pipes using Darcy-Weisbach equation.
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What are the characteristics of a laminar flow and turbulent flow? Discuss.
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