Section 8.3 Pressure and hydrostatic force
pressure = force per unit area = density * acceleration due to gravity * depth
System
Metric
American
density of water
1000 kg/m3 (or 1g/cm3)
62.4 lb/ft3
units of Force
newtons
pounds
area
m2
ft2
If pressure is constant over an area we have pressure = force/area which rearranges to F = Pressure * area
pressure
pascal or nt/m2
lb/ft2
We have two basic formulas:
Pressure = density * depth (* acceleration due to gravity if we are in the metric system)
Force = pressure * area
What is the pressure on a horizontal plate 2ft by 5ft located 3 feet below the
surface of water?
What is the total hydrostatic force on the plate? Note that pressure will be constant because the plate is horizontal.
What if we put the 2' x 5' plate so it is standing on its 5' side with its top still 3 feet below the surface of the water?
What about the total hydrostatic force on the plate?
How would this change if the top of the plate was even with the surface of the water?
8­3 #4 from your text:
The vertical plate shown is submerged in water.
Express the total hydrostatic force on the plate as an integral and evaluate it.
1 ft
3 ft
4 ft
#9 from your text: A vertical plate is submerged in water and has the indicated shape. Explain how to approximate the hydrostatic force against one side of the plate by a Riemann sum. Then express the force as an integral and evaluate it.
2 ft
10 ft
#2 from your text:
A tank is 8 m long, 4 m wide, 2 m high and contains kerosene with density 820 kg/m3 to a depth of 1.5 m. Find:
a) the hydrostatic pressure on the bottom of the tank
b) the hydrostatic force on the bottom, and
c) the hydrostatic force on one end of the tank.