Question

Question 1:

True or false. The no-slip boundary condition is only used in steady state problems.

Question 2:

Express in words the equation for conservation of mass for a pure fluid.

Question 3:

The shear stress required to detach endothelial cells in vitro is 26 Pa. A surgeon has invented a
catheter that can rotate once inside arteries. The idea of the catheter is to exert shear stresses
such that cells lining the artery are detached and the vessel ‘cleaned up’. Your job is to design
the size and speed of the catheter to reach the shear stress desired.

Answer 1

a) False, No slip condition is valid for unsteady state problems also. It say @ boundary the velocity is '0' b) Mass balance: mass entered into a system must be equal to mass leaving the system c_ T = 26 Pa mu = 3 times 10^-3 Kg/ms (Assumed viscosity of blood. Not sure where a catheter is used for sorry for the in continence) to find dv/dy v rightarrow m/s (Units) y rightarrow m (units) T = mu dv/dy dv/dy = T/mu = 26/3 times 10^-3 = 8666.67 1/s dv/dy = 8666.67 1/s dv = 8666.67 dy Integrating integral_0^v dV = 8666.67 integral_0^y dy v = 8666.67 y + c Applying No slip condition: @ y = 0 Rightarrow v = 0 0 = 8666.67 (0) + C c = 0 v = 8666.67 y The SIZe and speed are related by this equation