Π=μR4dp / dx()Q. Since there are no other dimensionless groups, a dimensionless relationship takes the form Π=μR4dp / dx()Q=Cwhere C is a constant. The flow rate is then given by Q=CR4μdpdx. We will show later this quarter that C=p/8, and the resulting expression is then known as the Hagen-Poiseuille equation. Note that the fluid density plays no role—why do you think that is? 5. a) Evaluate the dot product of a and b if a=xex+1−xy()ey+etezand b=2ex+3ey+ez. b) Find the magnitude of the vector a if a=cosθex+sinθey+ez. Solution
6. Find the component of the vector field a in the direction of the unit vector n, if a=xex+1−xy()ey+etezand n=22ex+22ey.