Question

Compare the differences in viscosity and density of water (SG = 1) and gasoline (SG = 0.803). Determine the pressure at the bottom of a 8m high tank that is filled with water, and compare it to the pressure at the bottom if the tank is filled with gasoline. Calculate the volumetric and mass flow rates of the two fluids in a 0.10m diameter pipe moving at a velocity of 4.2 m/s.

Answer 1

Ans 1

Viscosity of water = 10^-3 Pa-s

Density of water = specific gravity x density of water

= 1 x 1000 kg/m3 = 1000 kg/m3

Viscosity of gasoline = 2.90 x 10^-4 Pa-s

Density of gasoline = specific gravity x density of water

= 0.803 x 1000 kg/m3 = 803 kg/m3

On comparing density, water is heavier liquid than gasoline that's why in the mixture of gasoline and water, gasoline always float on the top of the water layer.

On comparing viscosity, viscosity of water > viscosity of gasoline.

Ans 2

Pressure at bottom filled with water

P = density x g x h = 1000 kg/m3 x 9.81 m/s2 x 8 m

= 78480 Pa

Pressure at bottom filled with gasoline

P = density x g x h = 803 kg/m3 x 9.81 m/s2 x 8 m

= 63019.44 Pa

Ans 3

Area of pipe = 3.14/4 * diameter x diameter

= 3.14/4 * 0.10*0.10

= 0.00785 m2

Volumetric flow = area x velocity

= 0.00785 m2 x 4.2 m/s = 0.03297 m3/s

Mass flow rate of water = density x volumetric flow

= 1000 kg/m3 x 0.03297 m3/s = 32.97 kg/s

Mass flow rate of gasoline = density x volumetric flow

= 803 kg/m3 x 0.03297 m3/s = 26.47 kg/s