To measure the mass flow rate of a fluid in a laminar flow through a circular tube, a hot wire type velocity anemometer is placed in the centre of the tube. Assume that the measuring station is far...

To measure the mass flow rate of a fluid in a laminar flow through a circular tube, a hot wire type velocity anemometer is placed in the centre of the tube. Assume that the measuring station is far from the entrance of the pipe, the velocity distribution is parabolic

where u
_max
is centre line velocity of the fluid, r is the radial distance from the centre of tube and D is pipe diameter :

(i) Derive an expression for average fluid velocity at the cross-section in terms of u_max
and D,

(ii) Obtain an expression for mass flow rate