Length is dx in Control volume. An incompressible fluid of negligible viscosity
ID: 1843248 • Letter: L
Question
Length is dx in Control volume.
An incompressible fluid of negligible viscosity is pumped at a total volume flow rate Q through a porous surface into a small gap located between two closely spaced parallel plates. The flow in the gap can be considered one-dimensional (i.e., velocity is constant along any vertical cross-section) and only has one velocity component along the x- direction. Perform a control volume analysis on the small volume of fluid of length dx located at a distance x to obtain an expression for the pressure variation dp/dx.Explanation / Answer
As we know,flow is Incompressible,the volume change is less or almost negligible with the effect of pressure.
We will take a control volume.This is an open system.
Therefore,Energy entering = Energy exiting.
As stated in figure,there is no velocity change in z direction.
DV/DZ =0
Taking gravity force into consideration, will only be effected in y direction.
By Cons of mass,
D/DT +(dvx/DX) + dvy/dy +dvz/dz =0, vy =vz=0,
dvx/dx =0
By Momentum balance,
Dvx/dt+vxdvx/dx+vy dvx/dy + vzdvx/dz = dp/dx +d^2vx/dx^2 + d^2vx/dy^2+d^2vx/dz^2 + gx
By simplifying we get
d^2vx/dy^2 = dp/dx
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.