1) Ignoring air pressure, show that the pressure caused by a column of water 1.0

Question

1) Ignoring air pressure, show that the pressure caused by a column of water 1.00 inches tall is equal to 248.9 Pa.

2) A smooth, thin, square piece of rubber, eight inches by eight inches, is sitting on a smooth table at sea level. What is the total force of the atmosphere on the material?

3) What is the change in weight of a hollow cylinder of height 10 cm and radius 4 cm when the air is pumped out of it?

4) Assume that there is a 30-foot difference in elevation between the first and the third floors of Thimann laboratories. What is the difference in atmospheric pressure between the two floors, expressed in inches of water? (In the real world, pressures are often expressed as "inches of water").

Explanation / Answer

part 1 )

P = rho*g*h

h = 1 inch = 0.0254 m

P = 10^3 * 9.8 * 0.0254

P = 248.9 Pa

part 2 )

F = PA

P = atmoshpheric pressure = 1.013 x 10^5 =

A = L^2

L = 8 inch = 0.2032 m

F = 4182.7 N

part 3 )

Volume of cylinder = pi*r^2*h

V = 160*pi *cm^3

density of of air = 0.00128 g/cm^3

Air pumped out of cylinder = 0.00128 * 160pi = 0.64 g

part 4)

P1 - P2 = rho * g(h2-h1)

1ft = 0.3048 m

dP = 1.2 * 9.8 * 30*0.3048

dP = 107.5 Pa

dP = rho_water *g*y = rho_air *g*h

y = rho_air * h/rho_water

y = 1.2 * 9.1 / 1000 = 0.011 m

y = 1.1 cm

1cm = 1/2.54 in = 0.39 inch

y = 1.1 * 0.39 = 0.43 inch

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