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If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.?
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If the velocity profile of a fluid over a plate is parabolic with the ...
Calculation of Velocity Gradient and Shear Stress on a Plate
Given:
Velocity profile of fluid over a plate is parabolic
Distance of vortex from the plate is 20cm
Velocity at the vortex is 120cm/s
Viscosity of fluid is 8.5 poise
Velocity Profile:
The velocity profile of fluid over a plate is given by the equation:
v = (2/3) * Uavg * [1 - (y/h)^2]
where, v is the velocity of fluid at a distance y from the plate, Uavg is the average velocity of fluid, and h is the distance of the plate from the center of the vortex.
Calculation of Uavg:
Since the velocity profile is parabolic, we can assume that the velocity at the center of the vortex is the maximum velocity i.e. 120 cm/s.
Therefore, Uavg = (3/2) * 120 = 180 cm/s.
Calculation of Velocity Gradient:
The velocity gradient is given by the formula:
du/dy = (4/3) * Uavg * (y/h)
where, du/dy is the velocity gradient.
At y = h, du/dy = (4/3) * Uavg = (4/3) * 180 = 240 cm/s^2.
Calculation of Shear Stress:
The shear stress on the plate is given by the formula:
tau = mu * du/dy
where, tau is the shear stress on the plate and mu is the viscosity of the fluid.
Substituting the values, we get:
tau = 8.5 * 240 = 2040 dyne/cm^2.
Therefore, the velocity gradient is 240 cm/s^2 and the shear stress on the plate is 2040 dyne/cm^2.
Given:
Velocity profile of fluid over a plate is parabolic
Distance of vortex from the plate is 20cm
Velocity at the vortex is 120cm/s
Viscosity of fluid is 8.5 poise
Velocity Profile:
The velocity profile of fluid over a plate is given by the equation:
v = (2/3) * Uavg * [1 - (y/h)^2]
where, v is the velocity of fluid at a distance y from the plate, Uavg is the average velocity of fluid, and h is the distance of the plate from the center of the vortex.
Calculation of Uavg:
Since the velocity profile is parabolic, we can assume that the velocity at the center of the vortex is the maximum velocity i.e. 120 cm/s.
Therefore, Uavg = (3/2) * 120 = 180 cm/s.
Calculation of Velocity Gradient:
The velocity gradient is given by the formula:
du/dy = (4/3) * Uavg * (y/h)
where, du/dy is the velocity gradient.
At y = h, du/dy = (4/3) * Uavg = (4/3) * 180 = 240 cm/s^2.
Calculation of Shear Stress:
The shear stress on the plate is given by the formula:
tau = mu * du/dy
where, tau is the shear stress on the plate and mu is the viscosity of the fluid.
Substituting the values, we get:
tau = 8.5 * 240 = 2040 dyne/cm^2.
Therefore, the velocity gradient is 240 cm/s^2 and the shear stress on the plate is 2040 dyne/cm^2.
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If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.?
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If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.?.
If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity profile of a fluid over a plate is parabolic with the vortex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress on the plate, if viscosity of the fluid is 8.5 poise.?.
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