Consider a laminar flow in a circular pipe with radius $R$ and length of $L.$

a$)$ Suppose you will simulate this flow using CFD$,$ sketch the domain to be simulated, and write

down the three boundary conditions needed to simulate this flow. $(4$ marks$)$

b$)$ Write down the governing equations required to solve this flow. How many equations will

need to be solved? $(4$ marks$)$

c$)$ Write down the equation to calculate the entrance length. $(1$ mark$)$

d$)$ Write down the equation for the velocity profile of a fully developed pipe flow. $(1$ mark$)$