Question

The velocity distribution of a laminar flow through a cylindrical tube is
A). Is constant over the cross-section
B). Varies linearly with zero at the walls to maximum at the centre
C). Varies parabolic with maximum at the centre.
D). None of these

Answer 1

Hint: The term laminar flow is distinguishing that flow by the momentum of the high diffusion and the momentum of the low convection. When, the fluid is flowing through the closed channel like a pipe.

Complete step by step solution:
The laminar flow usually happens when the fluid is moving slowly or it is very viscous.
The term Reynolds number, is the velocity is set on the dimensionless parameter, that characterizes the flow.
The flow rate of the liquid is measured as the volume of the liquid that moves in a definite amount of the time. It also depends on the area of the pipe as well as the channel of the liquid that is moving around. We can also calculate the flow in Liters per second.
In a laminar flow the velocity profile is given by
$v(x)\text{ = }{\text{v}}_m\left[1-{\displaystyle \frac{x^2}{R^2}}\right]$
Where, vm is the maximum speed of the fluid particle,
x is the distance from the centre of the tube
R is the radius of the tube
Distribution of v(x) is a parabolic with maximum value at x = 0
So, it varies parabolic with the maximum at the centre
So, the option (C) is correct.

Note: With the help of the Reynolds number we identify the type of the flow.
In laminar flow, the Reynolds number is less than 2000.
In Turbulent flow, the Reynolds number is greater than 3500.
In Transitional flow, the Reynolds number between 2000 and 3500.
If the Reynolds number is very small such as less than 1, then the fluid is revealed as well as flow.