We have a laminar fully developed channel flow of water with density = 1000 Kg/m3 and kinematic viscosity 1.3x10-6 m2/s. The velocity profile u is given as u/Umax=1-(y/h)2 where Umax is the centerline velocity and equal to 20 cm/s . The v and w components of the velocity are zero.
a) On the basis of dimensionality of the velocity profile what type of flow is this one i.e. 1-D, 2-D, unsteady etc. ?
b) What is the flow acceleration? Show the calculation term by term.
c) On the basis of result at B what can be said about sum of forces acting on a control volume(CV) ABCD shown in the figure? What type of forces are acting on the fluid?
d) What is the mass flow rate of the water in the channel? What is the relationship between average velocity and Umax?
e) What is the drag force exerted by the water on the top and bottom walls in the CV ABCD?
f) If the friction force on the side walls can be neglected because of their small area compared to the top and bottom walls, what is the net pressure force acting on CV ?
g) What is the rate of volume expansion of this flow? Show by using the equation which represents the rate of volume expansion.
h) Where would you observe this type of flow in practical engineering applications? Give one or two examples.