Introducing FluidsHydrostatic Pressure

Fluids

• Fluids are substances that can flow, such as liquids and gases, and even a few solids.

• In Physics B, we will limit our discussion of fluids to substances that can easily flow, such as liquids and gases.

Review: Density

• = m/V– : density (kg/m3)– m: mass (kg)– V: volume (m3)

• Units:– kg/m3

• You should remember how to do density calculations from chemistry!

Pressure• P = F/A– P : pressure (Pa)– F: force (N)– A: area (m2)

• Pressure unit: Pascal ( 1 Pa = 1 N/m2)• The force on a surface caused by pressure is always

normal (or perpendicular) to the surface. This means that the pressure of a fluid is exerted in all directions, and is perpendicular to the surface at every location.

balloon

Sample Problem• Calculate the net force on an airplane window if cabin pressure is

90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

Atmospheric Pressure

• Atmospheric pressure is normally about 100,000 Pascals.

• Differences in atmospheric pressure cause winds to blow.

Low atmospheric pressure inside a hurricane’s eye contributes to the severe winds and the development of the storm surge.

Hurricane Katrina’s Storm Surge

Mississippi River Gulf OutletNew Orleans East/St. Bernard Parish

The Pressure of a Liquid• P = gh – P: pressure (Pa)– : density (kg/m3)– g: acceleration constant (9.8 m/s2)– h: height of liquid column (m)

• This is often called hydrostatic pressure if the liquid is water. It excludes atmospheric pressure.

• It is also sometimes called gauge pressure, since a diver’s pressure gauge will read hydrostatic pressure. Gauge pressure readings never include atmospheric pressure, but only the pressure of the fluid.

• Absolute pressure is obtained by adding the atmospheric pressure to the hydrostatic pressure– pabs = patm + gh

Sample ProblemCalculate for the bottom of a 3 meter (approx 10 feet) deep swimming pool full of water: (a) hydrostatic pressure (b) absolute pressure(c)Which one of these represents the gauge pressure?

Hydrostatic Pressure in Dam Design

• http://www.iit.edu/~karagian/smart00/physics.html

The depth of Lake Mead at the Hoover Dam is 600ft. What is the hydrostatic pressure at the base of the dam?

Hydrostatic Pressure in Levee Design

Hurricane Katrina, August 2005

A hurricane’s storm surge can overtop levees, but a bigger problem can be increasing the hydrostatic pressure at the base of the levee.

New Orleans Elevation MapNew Orleans is largely below sea level, and relies upon a system of levees to keep the lake and the river at bay

Sample ProblemCalculate the increase in hydrostatic pressure experienced by the levee base for an expected (SPH Design: 11.5 ft) storm surge. How does this compare to the increase that occurred during Hurricane Katrina, where the water rose to the top of the levee (17.5ft)? (Normal Lake height is 1.0 ft)