This text is meant to accompany class discussions. It is not everything there is to know about fluids, hydrostatics, and fluid dynamics. It is meant as a prep for class.
This unit will describe concepts used in the study of fluids and properties of hydrostatics and fluid dynamics.
A fluid is any substance that fills the shape of its container and can flow.
Examples:
Water
Pepsi™, Coca-Cola™
Hand lotion
Gases such as air
A collection of very small marbles. (The smaller the marbles, the better they model the fluid.)
Mass Density
"Mass Density" describes how much mater you can pack into a volume. The mathematical symbol for density is the Greek letter , ρ -pronounced "rho."
The letter "rho" looks similar to the letter "p." Except "rho" is drawn more rounded at the top.
"ρ" is the Greek letter rho. It looks like a lower case "p," but is drawn with one motion by rounding off the top of the letter. "ρ" is the mass density in , "M" is the mass in [kg] and "V" is the volume in [m3.] As a matter of style the "V" is typically handwritten with serifs at the top. This is to further delineate it from the lower case "v" when it is handwritten.
When discussing fluids, mass density is often used in place of mass. For example:
Example Densities
Substance
"Air"
1.29
Granite
2700 (avg)
Helium
0.1686
Ice (fresh water)
916.7
Nitrogen
1.251
Water (fresh)
1000
Water (salt)
1029
Pressure
Pressure is defined as the number of molecular collisions per area. These collisions deliver a force to a surface. This becomes a simple formula:
Where:
"P" is a capital "P" and is the pressure measured in Pascals, "Pa." A Pascal is defined as a N/m2.
"F" is the force exerted on a surface of area "A." The force is measured in Newtons, N.
The area, A, is measured in meters2.
Rearranged,
F = PA
Given the same pressure the area becomes a force multiplier. Two sailboats who are identical in every way except one. One sailboat has a sail with 4 times the area. Given the same wind. The larger sail will receive 4 times the force from the wind.
Have you ever wondered why bicycle tires are pumped to a higher pressure than car tires. After all, they are skinnier tires.
You will discuss this in class. (I can't wait.)
Pressure's many units
While the Pascal is the standard unit of pressure, there several other ways of describing pressure and specifically the atmospheric pressure. Below is a table of those values.
Unit
Comment
atm
atmospheres (You live in a 1 atm space)
1 atm
1.0 x 105 Pa (This is a rounded value used on the AP exam and in class. For significant figure purposes, use it as if it is a counting number.*)
Pa
Pascal -standard S.I. unit
Pascal (It's equal to a Pascal) 1 atm = 1 x 105
760. mm mercury
The reported measurement on a mercury barometer that is equal to 1.0 x 105 Pa.
29.92 in mercury
The reported measurement on a mercury barometer that is equal to 1.0 x 105 Pa.
These are our typical units for 1 atmosphere of pressure. It is equal to 1.0 x 105 Pa
* 1 atmosphere of pressure is actually 1.01325 x 105 Pa. But the AP curriculum uses 100,000 Pa to make it easy to remember and work with.
Pressure and acceleration
When two forces are balanced, a body does not change velocity.
When two forces are unbalanced the velocity changes.
Think about the motion of sailboat. The area of both sides of a sail are equal. The pressure in front of the sail is caused by the air molecules hitting the sail. That makes it atmospheric pressure in front of the sail. When the wind blows from the back of the boat, the pressure on that side of the sail is atmospheric PLUS the extra pressure due to the wind. Because F=PA, a difference in pressure will be seen as a change in velocity.
The sailboat accelerates because of a difference in pressures between the front and back sides of the sailboat. The difference in pressure is called the gauge pressure. When the gauge pressure is equal to zero, nothing accelerates due to any pressure differences. When the magnitude of the gauge pressure is greater than zero you get an acceleration. (Note: You can get motion when the gauge pressure is zero. A body would move at a constant velocity. It cannot accelerate when the gauge pressure is zero.)
In the animation above the gauge pressure is the absolute value of PRIGHT - PLEFT. Therefore, in this animation, the gauge pressure is equal to PWIND.
Specific Gravity
If a fluid has a specific gravity < 1, then it is less dense than water. As an example, a specific density of 0.7 for a fluid means that the fluid floats on water and has a density of 700 kg/m3.
When water is pressed through the syringe, it generates a net, or gauge, pressure of 22,222 N/m. The area of the plunger where your thumb is pressed is 0.000225 m2. How much force did your thumb apply to the plunger?
Image: by U.S. Plastics: https://www.usplastic.com/catalog/images/products/Safety/400/17737psku.jpg Accessed 01/09/2021
When water is pressed through the syringe, it generates a net, or gauge, pressure of 22,222 N/m. The area of the plunger where your thumb is pressed is 0.000225 m2. How much force did your thumb apply to the plunger?
Image: by U.S. Plastics: https://www.usplastic.com/catalog/images/products/Safety/400/17737psku.jpg Accessed 01/09/2021
While playing some “street ball,” a large basketball player squishes a basketball when he sits on the ball to catch his breath. Just before being sat on, the ball was retrieved from some wet bushes and leaves a round imprint in the ground after being sat on. The basketball player sees this and starts to think. He pulls out his cellphone and using an app, determines the diameter of the wet circle on the pavement is 14 cm. After researching some values from the Internet, he determined his weight in pounds. How much did he weigh?
While playing some “street ball,” a large basketball player squishes a basketball when he sits on the ball to catch his breath. Just before being sat on, the ball was retrieved from some wet bushes and leaves a round imprint in the ground after being sat on. The basketball player sees this and starts to think. He pulls out his cellphone and using an app, determines the diameter of the wet circle on the pavement is 14 cm. After researching some values from the Internet, he determined his weight in pounds. How much did he weigh?
1. Search for the pressure in a basketball.
2. Use Google PSI to N/
m2.
3. Convert the diameter to a radius.
4. Convert the cm to m.
5. Calculate the area of the circle.
6.
Use Google to convert N to pounds.
(You should get an answer between 180 to 200 pounds.)
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
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, "M" is the mass in [kg] and "V" is the volume in [m3.] As a matter of style the "V" is typically handwritten with serifs at the top. This is to further delineate it from the lower case "v" when it is handwritten. 
While playing some “street ball,” a large basketball player squishes a basketball when he sits on the ball to catch his breath. Just before being sat on, the ball was retrieved from some wet bushes and leaves a round imprint in the ground after being sat on. The basketball player sees this and starts to think. He pulls out his cellphone and using an app, determines the diameter of the wet circle on the pavement is 14 cm. After researching some values from the Internet, he determined his weight in pounds. How much did he weigh?
