Chapter 5
Joseph F. Alward, PhD
Department of Physics
University of the Pacific
| Fluid
Mechanics Chapter 5
Joseph F. Alward, PhD |
|
Density
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Density = mass /
volume As bread is compressed, its volume decreases and density increases. ----------------------------------------- Example: mass = 300 kg volume = 0.3 m3 density = 600 kg / 0.3 m3 = 2000 kg / m3 |
| Material | Density (kg / m3) |
| Wood | 600 |
| Ice | 917 |
| Water | 1000 |
| Aluminum | 2702 |
| Iron | 7800 |
| Density of water = 1 gram /cm3 |
Weight Density
| Weight density = weight /
volume ----------------------------------------------------------------------- Example: Weight = 4000 N Volume = 2 m3 Weight density = 4000 N / 2 m3 = 2000 N / m3 |
Weight Density of Water
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One liter = 1000 cm3 ---------------------------------- Water: 1 g / cm3 1000 cm3 of water has a mass of 1000 g = 1 kg ---------------------------------- Weight = m g = 1 x 10 = 10 N ---------------------------------- Weight density of water: 10 N / liter |
Weight Density of Water
|
How many newtons per cubic meter? ----------------------------------
One liter = 1000 cm3 |
Number of liters in one cubic meter = 1,000,000 cm3 / 1000 cm3/liter = 1,000 liters ------------------------------------------------- Weight of one liter = 10 N Weight of 1 m3 = 10,000 N ---------------------------------------- What's the weight in tons of a cubic meter of water? |
Pressure
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Pressure = force /
area -------------------------------------- Books each exert the same force on table. Which one exerts the greater pressure? --------------------------------------
1 pascal = 1 N / m2 |
A Bed of Nails
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Would the pressure be greater, less, or the same if there were only one nail in each board? |
Pressure in a Liquid
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Pressure depends only on the depth below the surface. |
Pressure on Dams
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Liquid Pressure = Weight density x depth
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Water Pressure Example
| What is the pressure 10 m (33 feet) below the surface of water? ------------------------------------------------- Pressure = weight density x depth = (10,000 N / m3) (10 m) = 100,000 N / m2 |
Pressure in a Liquid
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Liquid pressure acts in all directions. What would happen to the object in the picture if the resultant forces on each side weren't perpendicular to the sides, i.e, they had a sideways component? |
Pressure Increases with Depth
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What happens to the range of each stream as time passes? |
Pressure Increases with Depth
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Why are the metal bands around the water tower closer together at the bottom? |
Buoyancy in a Liquid
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Pressure is greater at the bottom of the object because the depth is greater. A "buoyant" force acts on the object. |
Calculating the Buoyant Force
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Archimede's Principle:
The buoyant force is equal to the weight |
Calculating Buoyant Forces
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Buoyant force = weight of liquid displaced. ----------------------------------------------------------
How much force would it take to hold an
What force would be needed to hold a |
Buoyant Force Equals Weight of Liquid Displaced
 |
Buoyancy
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Buoyant force is due to pressure difference between top and bottom of object. Pressure difference does not depend on depth. |
Buoyancy
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Weight of water displaced equals the weight of the cargo. |
Flotation Depends on Density
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Object at left has density greater than water's; it sinks.
Object at the right has |
Density and Buoyancy
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Average density is less than water's. |
| Aluminum is less dense than iron.
Which displaces more water, iron, |
Buoyancy Question
| If an iron bar floating on a plank of wood in a swimming pool falls into the water, does the water level in the pool rise, drop, or remain the same? See hint below. |
Hint for Iron Buoyancy Question
| While on the plank, the iron displaces its weight
in water, but on the bottom of the pool it displaces its volume. Which is more: the water displaced when the iron was on the plank, or the water displaced by the sunken iron? |
Eureka!
 |
24 K gold is pure, 18 K is a mixture of gold and silver. Silver is less dense than gold. Consider equal masses of 18 K and 24 K gold: Which would displace more water? |
Pressure Increases with Density
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More air molecules means that more collisions with the tire wall occur each second. |
Pressure and Volume
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If the mass and temperature is held constant:
PV = constant
If the pressure is doubled,
If the pressure is halved, |
Atmospheric Pressure
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Atmosphere is about thirty miles thick, less dense at the top, more dense near the earth. ------------------------------- At sea level, air pressure is about 100,000 N / m2, or about 15 pounds/in2. ------------------------------- Hemispheres had areas of about 1/4 square meter. |
Atmospheric Pressure
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What is the origin of the force supporting the weight? ---------------------------------------- What, if anything, would happen to the weight if the system were taken to the top of a very tall mountain? |
Atmospheric Pressure
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The weight of a one-square meter column of air 30 miles tall is about 100,000 N, or about 25,000 pounds. ---------------------------------------------- Why doesn't the pressure of the atmosphere break windows? ---------------------------------------------- At what temperature would water boil in a vacuum? ---------------------------------------------- What would happen to the blood in the veins of a human placed in a vacuum? |
A Barometer
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Mercury is 13.6 times as dense as water. How tall a column of water could be supported by atmospheric pressure? -------------------------------------------------------- Would the mercury remain in the column if a hole were made in the top of the tube? |
How Straws Work
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What is the longest straw that would work? |
Water Pumps
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10.3 meters (about 33 feet) is the farthest water can be lifted by a vacuum pump. |
A Vacuum Pump
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Buoyancy in a Gas
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When, if ever, does the helium-filled balloon stop rising? Assume the balloon's size doesn't change. ------------------------------------------------- |
Bernoulli's Principle
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When the speed of a fluid increases, the internal pressure decreases. -------------------------------------------------- |
Streamlines
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If the opening is made more narrow, speed increases.
Pressure inside the fluid drops, |
Applications
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Moving air over the top of the paper is at a lower pressure than the stationary air under the paper. |
Bernoulli's Effect
 Crowding of streamlines increases the air speed, making the pressure difference greater than it would be for a flat roof. |
 Streamline crowding over an airplane wing. |
Bernoulli's Effect in Baseball
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Bernoulli's Principle
 Water pressure between boats is less than pressure on the outside of boats. |
Bernoulli's Principle
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Top of umbrella acts like an airplane wing. |
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