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A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.?
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A horizontal pipe of 5 cm diameter conveys an oil of specific gravity ...
Calculations for Oil Flow in Horizontal Pipe
Flow Rate and Center Line Velocity
- The area of the pipe is A = πr² = π(0.025m)² = 0.00196 m²
- The volumetric flow rate of oil is Q = Av = π(0.025m)² * v = 0.00196 m² * v
- The mass flow rate of oil is m = ρQ = 0.9 * 0.00196 m² * v = 0.001764 kg/s
- The center line velocity is v = Q/A = (20 kN/m²)/(0.5 * 0.8 kg/ms * 0.00196 m²) = 0.352 m/s
Wall Shear Stress and Frictional Drag
- The Reynolds number is Re = ρvd/μ = 0.9 * 0.352 m/s * 0.05 m / 0.8 kg/ms = 19.95
- The friction factor for laminar flow is f = 64/Re = 3.202 x 10^-3
- The wall shear stress is τw = fρv²/2 = 3.202 x 10^-3 * 0.9 * (0.352 m/s)² / 2 = 0.021 N/m²
- The frictional drag over 100 m of pipe length is F = τw * πdL = 0.021 N/m² * π * 0.05 m * 100 m = 33.183 N
Power of Pump Required
- The power required by the pump is P = Fv/η = 33.183 N * 0.352 m/s / 0.6 = 19.376 W
Velocity and Shear Stress Near Pipe Surface
- The velocity at 1 cm from the pipe surface is v' = v/2 = 0.176 m/s
- The shear stress at 1 cm from the pipe surface is τw' = τw(2/3 + 0.11Re^-0.25) = 0.021 N/m² * (2/3 + 0.11 * 19.95^-0.25) = 0.028 N/m²
Overall, these calculations provide important information for designing and operating a horizontal pipe system for transporting oil. The flow rate and center line velocity indicate how much oil can be transported and at what speed, while the wall shear stress and frictional drag provide insight into the forces that must be overcome to maintain flow. The power of the pump required is a key factor in determining the energy needed to maintain flow, while the velocity and shear stress near the pipe surface can help ensure that the oil is flowing smoothly and without damage to the pipe system.
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A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.?
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A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.?.
A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.?.
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A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.?, a detailed solution for A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.? has been provided alongside types of A horizontal pipe of 5 cm diameter conveys an oil of specific gravity 0.9 and dynamic viscosity 0.8 kg/ms. Measurements indicate a pressure drop of 20 kN/m2 per metre of pipe length traversed. Make calculations for the (i) flow rate of oil and centre line velocity, (ii) wall shear stress and the frictional drag over 100 m of pipe length, (iii) power of pump required assuming an overall efficiency of 60 percent, (iv) the velocity and shear stress at 1 cm from the pipe surface.? theory, EduRev gives you an
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