Mechanical Properties of Fluids — Practice

Question 1

Find the pressure at the bottom of a 10 m water tank (rho = 1000, P0 = 1e5 Pa, g = 10).

Accepted Answer

P = P0 + rho g h = 1e5 + 1000 x 10 x 10 = 2e5 Pa (2 atm).

Question 2

A hydraulic lift has piston areas 10 cm^2 and 500 cm^2. Find the force on the small piston to lift 2000 kg.

Accepted Answer

F2 = mg = 20000 N. F1 = F2 x A1/A2 = 20000 x 10/500 = 400 N.

Question 3

A 1 mm sphere (rho = 5000) falls through water (rho = 1000, eta = 0.001 Pa s, g = 10). Find terminal velocity.

Accepted Answer

v_t = (2/9)(rho_s - rho_f)g r^2/eta = (2/9)(4000)(10)(1e-6)/0.001 = (2/9)(40) = 8.89 m/s.

Question 4

An object weighs 50 N in air and 30 N in water. Find its volume and density.

Accepted Answer

Buoyant force = 20 N = rho V g, so V = 20/(1000 x 10) = 0.002 m^3. Density = mass/V = (50/10)/0.002 = 2500 kg/m^3.

Question 5

Water rises 5 cm in a capillary. If the radius is halved, what is the new rise?

Accepted Answer

h is inversely proportional to r, so halving the radius doubles the rise to 10 cm.

Practice — Mechanical Properties of Fluids