For fully developed laminar pipe flow in a circular pipe, the velocity profile is u(r) = 2(1-r2 /r2 ) in m/s, where r is the inner radius of the pipe. assuming the pipe diameter is 4 cm, find the maximum and average velocities in the pipe as well as the volume flow rate

a)

b)

c) Q = 1.256 × 10⁻³ m³/s

Explanation:

Given:

The velocity profile as:

Now, the maximum velocity of the flow is obtained at the center of the pipe

i.e r = 0

thus,

or

Now,

or

or

Now, the flow rate is given as:

Q = Area of cross-section of pipe ×

or

Q =

or

Q =

or

Q = 1.256 × 10⁻³ m³/s

c) up is the direction the magnetic force is acting on the charge.