CHEMICAL ENGINEERING

286 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 11.2

Water flows at a velocity of 1 m/s over a plane surface 0.6 m wide and 1 m long. Calculate
the total drag force acting on the surface if the transition from streamline to turbulent
flow in the boundary layer occurs when the Reynolds groupRexD 105.

Solution

See Volume 1, Example 11.1

PROBLEM 11.3

Calculate the thickness of the boundary layer at a distance of 150 mm from the leading
edge of a surface over which oil, of viscosity 50 mN s/m^2 and density 990 kg/m^3 ,flows
with a velocity of 0.3 m/s. What is the displacement thickness of the boundary layer?

Solution

See Volume 1, Example 11.2

PROBLEM 11.4

Calculate the thickness of the laminar sub-layer when benzene flows through a pipe
50 mm diameter at 0.003 m^3 /s. What is the velocity of the benzene at the edge of the
laminar sub-layer? Assume fully developed flow exists within the pipe.

Solution

See Volume 1, Example 11.3

PROBLEM 11.5

Air is flowing at a velocity of 5 m/s over a plane surface. Derive an expression for the
thickness of the laminar sub-layer and calculate its value at a distance of 1 m from the
leading edge of the surface.
Assume that within the boundary layer outside the laminar sub-layer, the velocity of
flow is proportional to the one-seventh power of the distance from the surface and that
the shear stressRat the surface is given by:

R/u^2 s D 0. 03 

usx/   ^0.^2

whereis the density of the fluid (1.3kg/m^3 for air), is the viscosity of the fluid
(17ð 10 ^6 Ns/m^2 for air),usis the stream velocity (m/s), andxis the distance from
the leading edge (m).