Question

A box-shaped metal can has dimensions 6 in by 2 in by 12 in high. All of the air inside the can is removed with a vacuum pump. Assuming normal atmospheric pressure outside the can.
a. Find the total force on one of the 6 in by 12 in sides.
b. Find the gauge pressure at the bottom of a swimming pool that is 17 feet deep.

Answer 1

Answer:

a) The total force is 4659.8 N

b) The gauge pressure is 50764 Pa

Explanation:

Given:

Pressure inside = 0

Patm = pressure outside = 1.013x10⁵Pa

Pressure difference = ΔP = 1.013x10⁵ - 0 = 1.013x10⁵Pa

a) The area is equal:

$A=12*6=72in^{2} =0.046m^{2}$

The force is:

$F=delta-P*A=1.013x10^{5} *0.046=4659.8N$

b) The gauge pressure at the bottom is equal:

$P=\rho gh$

Where:

ρ = density = 1000 kg/m³

h = 17 ft = 5.18 m

Replacing:

$P=1000*9.8*5.18=50764Pa$