Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II Year FLUID MECHANICS – I Previous Question Paper (March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Calculate specific weight, density and specific gravity of two liters of a liquid which weigh 15 N.
Answer
Given data:
- Volume of liquid (V) = 2 liters = 2 × 10-3 m3
- Weight of liquid (W) = 15 N
1. Specific Weight (γ):
Specific weight is defined as the weight per unit volume of a fluid.
2. Density (ρ):
Density is the mass per unit volume. Since W = mg, mass m = W / g. Taking g = 9.81 m/s2:
3. Specific Gravity (S):
Specific gravity is the ratio of the density of the liquid to the density of water (ρw = 1000 kg/m3).
Define pressure. Obtain an expression for the pressure intensity at a point in a fluid.
Answer
Pressure is defined as the normal force exerted by a fluid per unit area. Mathematically, if a force dF acts on an area dA, the pressure p is given by p = dF/dA.
To obtain the expression for pressure intensity at a point in a static fluid, consider a small fluid element of prism shape with sides dx, dy, and dz. Let the pressure intensities on the faces be px, py, and ps.
- Forces in x-direction: px(dy × dz) - ps(ds × dz) sin θ = 0
- Forces in y-direction: py(dx × dz) - ps(ds × dz) cos θ - (Weight of element) = 0
Since sin θ = dy/ds and cos θ = dx/ds, substituting these into the x-direction equation gives:
Similarly, for the y-direction, as the volume of the element approaches zero, the weight term becomes negligible, leading to:
Thus, at any point in a static fluid, the pressure intensity is equal in all directions: px = py = ps. This is known as Pascal's Law.
Show that the rate of increase of pressure in a vertical direction in a fluid at rest is equal to the weight density of the fluid at that point.
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A vertical cylinder of diameter 180 mm rotates concentrically inside another cylinder of diameter 181.2 mm. The space between the cylinder is filled with the oil whose viscosity is 8 poise. Find out the power required to rotate the cylinder at 100 rpm.
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Explain the terms: (i) Path line (ii) Streak line (iii) Stream line (iv) Stream tube.
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A pipe, through which water is flowing, is having diameters 40 cm and 20 cm at the cross-sections 1 and 2 respectively. The velocity of water at section 1 is 5 m/s. Find the velocity head at the sections 1 and 2 and also rate of discharge.
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Define stream function and velocity potential. What are their uses?
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Determine whether the following velocity components satisfy the continuity equation: (i) u = cx, v = -cy (ii) u = -cx/y, v = c log xy.
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What are the applications of Momentum equation? Explain.
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Describe the procedure of finding the forces on pipe bend.
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State the assumptions made in the derivation of Bernoulli’s equation. State the momentum equation and explain its significance.
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A 30 cm diameter horizontal pipe terminates in a nozzle with the exit diameter of 7.5cm. If the water flows through the pipe at the rate of 0.15 m3/s. What force will be exerted by the fluid on the nozzle?
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What factors account for the loss of energy in laminar flow? How does the energy loss vary with velocity of flow?
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A liquid with a specific gravity 2.8 and a viscosity 0.8 poise flows through a smooth pipe of unknown diameter, resulting in a pressure drop of 800 N/m2 in 2 km length of the pipe. What is the pipe diameter if the mass flow rate is 2500 kg/hr.
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It is required to determine the frictional drag of a submarine. The length of the hull is 75m and its surface area is 3000m2. The submarine is travelling at a constant speed of 5m/s. critical Reynolds number at which the flow in the boundary layer changes from laminar to turbulent is 5 × 10^5. Assuming that the boundary layer at the leading edge is laminar, obtain the frictional drag and the power required to propel the submarine at 5m/s. Take kinematic viscosity = 1 × 10^-6 m2/s and density = 1000 kg/m3.
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