Page 32 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 13

T

Figure 1.3 Flow between parallel plates.

a) For the coordinate system shown in Figure 1.3 (b), show that the velocity
distribution takes the form

b) Calculate the volumetric flow rate by using the velocity distributions given
above. What is your conclusion?

Answer: b) For both cases & =

1.7 An incompressible Newtonian fluid flows in the z-direction through a straight
duct of triangular cross-sectional area, bounded by the plane surfaces y = H,
y = fix and y = - fix. The velocity distribution under steady conditions is
given by
PPI
= -
21, (9 - H) (3x2 - y2)
4 pLH
Calculate the volumetric flow rate.

Answer: &=
180 pL