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A fully developed laminar viscous flow through a circular tube has the ratio of maximum velocity to average velocity as
- a)3.0
- b)2.0
- c)2.5
- d)1.5
Correct answer is option 'B'. Can you explain this answer?
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The ratio of maximum velocity to average velocity in a fully developed laminar viscous flow through a circular tube can be determined using the Hagen-Poiseuille equation. This equation relates the fluid flow rate to the pressure drop across the tube and the tube geometry.
1. Hagen-Poiseuille equation:
The Hagen-Poiseuille equation for laminar flow through a circular tube is given by:
Q = (π * r^4 * ΔP) / (8 * μ * L)
Where:
- Q is the volumetric flow rate
- r is the radius of the tube
- ΔP is the pressure drop across the tube
- μ is the dynamic viscosity of the fluid
- L is the length of the tube
2. Maximum velocity:
The maximum velocity occurs at the centerline of the tube and can be calculated using the equation:
Vmax = (2 * Q) / (π * r^2)
3. Average velocity:
The average velocity can be determined by dividing the volumetric flow rate by the cross-sectional area of the tube:
Vavg = Q / (π * r^2)
4. Ratio of maximum velocity to average velocity:
To find the ratio of maximum velocity to average velocity, we can substitute the expressions for Q in the above equations:
Vmax / Vavg = [(2 * Q) / (π * r^2)] / [Q / (π * r^2)]
Simplifying the equation, we get:
Vmax / Vavg = 2
Therefore, the correct answer is option 'B' - 2.0. The ratio of maximum velocity to average velocity in a fully developed laminar viscous flow through a circular tube is 2.0.
1. Hagen-Poiseuille equation:
The Hagen-Poiseuille equation for laminar flow through a circular tube is given by:
Q = (π * r^4 * ΔP) / (8 * μ * L)
Where:
- Q is the volumetric flow rate
- r is the radius of the tube
- ΔP is the pressure drop across the tube
- μ is the dynamic viscosity of the fluid
- L is the length of the tube
2. Maximum velocity:
The maximum velocity occurs at the centerline of the tube and can be calculated using the equation:
Vmax = (2 * Q) / (π * r^2)
3. Average velocity:
The average velocity can be determined by dividing the volumetric flow rate by the cross-sectional area of the tube:
Vavg = Q / (π * r^2)
4. Ratio of maximum velocity to average velocity:
To find the ratio of maximum velocity to average velocity, we can substitute the expressions for Q in the above equations:
Vmax / Vavg = [(2 * Q) / (π * r^2)] / [Q / (π * r^2)]
Simplifying the equation, we get:
Vmax / Vavg = 2
Therefore, the correct answer is option 'B' - 2.0. The ratio of maximum velocity to average velocity in a fully developed laminar viscous flow through a circular tube is 2.0.
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A fully developed laminar viscous flow through a circular tube has the ratio of maximum velocity to average velocity asa)3.0b)2.0c)2.5d)1.5Correct answer is option 'B'. Can you explain this answer?
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