Question

1) 25pt)Poiseuille’s Law is a fundamental law of fluid dynamics that describes the flow velocity of a viscous incompressible fluid in a cylinder. It says that in a cylinder of radius R and length L, the velocity of the fluid r (where r ≤ R) units from the center line of the cylinder is: ? = ? 4?? (? 2 − ? 2 ), where P is the difference in the pressure between the ends of the cylinder and ν is the viscosity of the fluid. Assuming P and ν are constant, the velocity V along the center line of the cylinder (r = 0) is V = kR2 /L, where k is a constant that we will take to be k =1 . i) Estimate the change in the centerline velocity (r = 0) if the radius of the flow cylinder increases from R = 3.00 cm to R = 3.05 cm. and the length increases from L = 50.0 cm to L = 50.5 cm. ii) Estimate the percent change in the centerline velocity if the radius of the flow cylinder R decreases by 1% and the length increases by 2%. iii) If the radius of the cylinder increases by p%, then the length of the cylinder must increase by approximately what percent in order that the velocity remain constant?

Answer 1

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