Consider the following statements regarding the laminar flow through a...
For laminar flow th rough circular pipe
It is neither constant, and does not depend on pipe roughness.
As head loss varies directly with mean velocity so pressure drop also.
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Consider the following statements regarding the laminar flow through a...
Friction factor:
The friction factor in laminar flow through a circular pipe is not constant. It depends upon the pipe roughness. As the roughness of the pipe increases, the friction factor also increases. This is because the roughness of the pipe creates more resistance to the flow of the fluid, resulting in a higher friction factor.
Reynolds number:
The friction factor also varies inversely with the Reynolds number of flow. The Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow. In laminar flow, the Reynolds number is low, and as the Reynolds number increases, the flow transitions from laminar to turbulent. As the Reynolds number increases, the friction factor decreases.
Velocity distribution:
In laminar flow through a circular pipe, the velocity distribution is indeed parabolic. This means that the velocity of the fluid is maximum at the center of the pipe and decreases towards the pipe walls. The velocity profile follows a parabolic shape, with the maximum velocity occurring at the centerline of the pipe.
Pressure drop:
The pressure drop in laminar flow through a circular pipe varies directly with the mean velocity. As the mean velocity of the fluid increases, the pressure drop also increases. This is because the increase in velocity leads to a higher resistance to flow, resulting in a higher pressure drop.
Summary:
From the given statements:
- Statement 1 is incorrect. The friction factor is not constant; it depends on the pipe roughness.
- Statement 2 is correct. The friction factor does depend on the pipe roughness.
- Statement 3 is correct. The friction factor varies inversely with the Reynolds number.
- Statement 4 is correct. The velocity distribution in laminar flow is parabolic.
- Statement 5 is incorrect. The pressure drop varies directly with the mean velocity.
Therefore, the correct statements are 2 and 3, or 2 and 4, or 3 and 4. The correct answer is option D.
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