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Laminar flow is taking place in a pipe of diameter 0.3 m. The maximum velocity is 1.8 m/s. Then mean velocity is
- a)0.9 m/s
- b)1.8 m/s
- c)0.6 m/s
- d)0.8 m/s
Correct answer is option 'A'. Can you explain this answer?
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Laminar flow is taking place in a pipe of diameter 0.3 m. The maximum...
For a fully developed laminar viscous flow through a circular pipe, the ratio of maximum velocity to average velocity is 2.
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Note: For laminar flow between two fixed parallel plates
uavg = 2umax/3
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Laminar flow is taking place in a pipe of diameter 0.3 m. The maximum...
Laminar Flow in a Pipe
In laminar flow, the fluid moves in smooth, parallel layers with little to no mixing between them. This type of flow occurs at low velocities and is characterized by a well-defined flow pattern. The flow in a pipe can be classified as laminar or turbulent based on the Reynolds number (Re).
Reynolds Number
The Reynolds number is a dimensionless parameter that determines the flow regime. It is defined as the ratio of inertial forces to viscous forces and is given by the formula:
Re = (ρvd) / μ
Where:
- Re is the Reynolds number
- ρ is the density of the fluid
- v is the velocity of the fluid
- d is the diameter of the pipe
- μ is the dynamic viscosity of the fluid
Mean Velocity in Laminar Flow
In laminar flow, the velocity of the fluid is not constant across the pipe cross-section. The maximum velocity occurs at the center of the pipe, while the velocity is lower near the pipe walls. However, the mean velocity is the average velocity of the fluid across the pipe cross-section and can be calculated using the formula:
Vmean = (1/2) * Vmax
Where:
- Vmean is the mean velocity
- Vmax is the maximum velocity
Calculating Mean Velocity
Given:
- Diameter of the pipe (d) = 0.3 m
- Maximum velocity (Vmax) = 1.8 m/s
Using the formula for mean velocity, we can calculate:
Vmean = (1/2) * Vmax
= (1/2) * 1.8
= 0.9 m/s
Therefore, the correct answer is option 'A' - 0.9 m/s.
In laminar flow, the fluid moves in smooth, parallel layers with little to no mixing between them. This type of flow occurs at low velocities and is characterized by a well-defined flow pattern. The flow in a pipe can be classified as laminar or turbulent based on the Reynolds number (Re).
Reynolds Number
The Reynolds number is a dimensionless parameter that determines the flow regime. It is defined as the ratio of inertial forces to viscous forces and is given by the formula:
Re = (ρvd) / μ
Where:
- Re is the Reynolds number
- ρ is the density of the fluid
- v is the velocity of the fluid
- d is the diameter of the pipe
- μ is the dynamic viscosity of the fluid
Mean Velocity in Laminar Flow
In laminar flow, the velocity of the fluid is not constant across the pipe cross-section. The maximum velocity occurs at the center of the pipe, while the velocity is lower near the pipe walls. However, the mean velocity is the average velocity of the fluid across the pipe cross-section and can be calculated using the formula:
Vmean = (1/2) * Vmax
Where:
- Vmean is the mean velocity
- Vmax is the maximum velocity
Calculating Mean Velocity
Given:
- Diameter of the pipe (d) = 0.3 m
- Maximum velocity (Vmax) = 1.8 m/s
Using the formula for mean velocity, we can calculate:
Vmean = (1/2) * Vmax
= (1/2) * 1.8
= 0.9 m/s
Therefore, the correct answer is option 'A' - 0.9 m/s.
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