October 16: Balloons − Pressure and density Chapter 5 Fluids October 16: Balloons − Pressure and density

Characteristics of the air The air is a gas. It has no fixed shape. What else has no fixed shape? The air consists of individual atoms and molecules. What kind of molecules are they? The particles of the air hold thermal energy. Thermal energy includes internal kinetic energy and internal potential energy. The particles of the air are in frenetic thermal motion. They collide with each other and bounce on the wall of the container very often.

Air pressure The air particles transfer momentum when they bounce off the wall of the container. Each momentum transfer involves forces. Bouncing particles thus exert forces on the wall of the container. The average force on the wall is proportional to the surface area. The average force per unit area is called pressure:

More about air pressure The SI unit of pressure is newton/meter2, or Pascal, abbreviated Pa. In practice pressure has a lot of units. Examples are: pound-per-square-inch (psi), atmosphere, Torr, bar, mmHg, and inHg. One atmosphere is about 100,000 Pa. (The more exact value is 101325 Pa). It is about putting 2 lb of weight on one of your nails, although you do not actually feel it. The air pressure is exerted on everything immerged in the air.

Density The density of a substance is its mass per unit volume: The SI unit of density is kg/m3. The density of the air around us is about 1.25 kg/m3. What is the density of water?

(in grams per cubic centimeter) TABLE OF DENSITY FOR SOME COMMON MATERIALS (in grams per cubic centimeter) COMMON MATERIALS Water ………………………1.00 Glass………………………2.60 Granite……………………...2.650 Bone……………………….1.85 Human Body………………..0.995 Butter……………………...0.94 Ice…………………………...0.917 Carbon…………………….2.60 Kerosene……………………0.800 Chalk………………………2.36 Salt………………………….2.200 Coal………………………..1.50 Sand…………………………2.800 Cork………………………..0.25 Sulfuric Acid………………..1.840 Gasoline……………………0.72 COMMON METALS Aluminum…………………..2.70 Mercury……………………13.60 Brass………………………...8.40 Nickel………………………8.80 Chromium…………………..7.10 Platinum……………………21.50 Copper………………………8.63 Silver……………………….10.40 Gold…………………………19.30 Tin………………………….7.30 Iron………………………….7.80 Uranium……………………18.70 Lead…………………………11.30 Zinc…………………………6.90 Magnesium………………….1.74 SOME COMMON WOODS Alder………………………0.40 White Pine…………………0.43 Ash………………………..0.75 Maple………………………0.69 Balsa………………………0.12 Oak…………………………0.85 Douglass fir……………….0.56 Yellow Pine………………...0.46 Ebony……………………..1.20 Walnut……………………..0.67 Larch (tamarack)………..0.51

Temperature The average thermal kinetic energy per particle is proportional to the absolute temperature of the air. The SI unit of the absolute temperature is Kelvin, or K. 0 K is the absolute zero, where there is no thermal energy. Step sizes: 1 K step is the same as 1 °C step. Relations: Question: What is the room temperature measured in the absolute temperature?

Air pressure and density In denser air, the particles hit the surface more often, which results in a larger pressure. The air pressure is proportional to its density. Air pressure and temperature The faster particles hit surface harder and more frequently. Therefore the hotter air has a larger pressure. The air pressure is proportional to its absolute temperature.

Read: Ch5: 1 Homework: Ch5: E3,7 Due: October 27

October 18: Balloons −Buoyancy

Demo: The Magdeburg hemispheres Otto von Guericke, 1650

Question: The Magdeburg hemispheres have a diameter of 0.5 m. How much force is needed to separate them? Answer: Pressure = 1 atmosphere = 100,000 Pa. Force = Pressure × Area =100,000 Pa ×p ×(0.5 m/2)2 ≈ 20,000 N ≈ 4,500 lbf. You can separate them if you could lift your car!

The atmosphere The atmosphere is in a stable equilibrium. The air pressure decreases with altitude. The pressure difference pushes each air layer upward. This upward force balances the layer’s weight, so that the air does not drop. The air near the ground supports the air overhead. The atmosphere has a structure. Near the ground the air pressure and the air density are the highest.

Question: An empty plastic bottle is sealed at the top of a mountain and is then brought to the sea level. What will happen to the bottle? Answer: The increase in atmospheric pressure will crush the bottle.

Buoyant Force Because of the structure of the atmosphere, the air pressure is stronger near the bottom of a balloon, and is weaker near the top of the balloon. Therefore the air pushes the balloon up harder than it pushes the balloon down. The difference between the upward and downward forces yields a net upward force, which is called the buoyant force.

Archimedes’ Principle An object fully or partially immersed in a fluid receives an upward buoyant force equal to the weight of the fluid it displaces.

Questions: 1. Two similar pieces of metal blocks are immersed in liquids, one in water and the other in oil. Compare the buoyant forces they experience. 2. A wood block and a metal block have the same volume. They are both fully immersed in water. Compare the buoyant forces they experience.

Read: Ch5: 1 Homework: Ch5: E9;P3 Due: October 27

October 23: Balloons − Hot air balloons and helium balloons

Hot air balloons For a gas: pressure  density × absolute temperature The average density of a hot air balloon is less than the density of the surrounding air. The hot air balloon weighs less than the air it displaces. That is, its weight is less than the buoyant force it receives. Therefore the hot air balloon experiences an upward net force and floats in the air. Movie: Hot air balloon I Movie: Hot air balloon II

Pressure and particle density The average number of gas particles per unit volume is called the particle density of the gas. All gas particles contribute equally to the pressure. Lower-mass particles travel faster and bounce more, but each bounce produces a weaker force. Higher-mass particles travel slower and bounce less, but each bounce produces a stronger force. Gases with equal particle densities and equal temperatures have equal pressures.

The Ideal Gas Law Gases with equal particle densities and equal temperatures have equal pressures. Boltzmann constant = 1.381 × 10-23 Pa · m3/K.

Question: You take an air-filled plastic container out of a refrigerator. The container warms up from 2 °C to 25 °C. How much does the pressure of the air in the container change? Answer:

Helium balloons The mass of a helium atom is less than an air particle: 4:29. At the same temperature, a helium balloon has similar pressure as the surrounding air. According to the ideal gas law, the helium has the same particle density as the surrounding air. The mass of the helium gas is less than the mass of the air it displaced. That is, the weight of the helium balloon is less than the buoyant force it receives. Therefore the helium balloon experiences an upward net force and floats in the air.

The hot air balloon and the helium balloon

Read: Ch5: 1 Homework: Ch5: E15;P5 Due: November 3

October 25: Water Distribution − Pressure and energy

Water moving in a horizontal pipe (no gravity effect) Everything obeys Newton’s laws of motion! When water experiences zero net force, it is still or it coasts. When water experiences a net force, it accelerates. Pressure imbalance exerts a net force on water. Water accelerates toward the lower pressure.

Pressurizing water Pascal’s principle: Water is incompressible. To pressurize water, you confine it and squeeze it. As you push inward on the water, it pushes outward on you. This outward push by water is its pressure. The water’s pressure rises as you squeeze it harder. The pressure increases uniformly throughout the water bottle: Pascal’s principle: A change in the pressure of an enclosed incompressible fluid is conveyed undiminished to every part of the fluid and to the surfaces of its container.

Pumping water A reciprocating piston pump: Draw the piston outward. Water flows from the low-pressure region into the cylinder. Push the piston inward. Water flows from the cylinder to the high-pressure region. You do work in both ways.

Work done in pumping water The pressurized water carries your work with it. This work is called “pressure potential energy”.

Pressure potential energy Question: Where does your work go when you are pumping water ? Steady state flow: When the flow rate does not change with time, we have a steady state flow. In a steady state flow the concept of pressure potential energy is meaningful.

Water energy in a streamline (no gravity effect) Stream line: The path of a water flow. Water in a steady state flow along a streamline has both pressure potential energy and kinetic energy. The total energy per volume must be a constant:

Read: Ch5: 2 Homework: Ch5: P11 Due: November 3

October 30: Water Distribution − Bernoulli’s equation

Gravity and water pressure The pressure of stationary water increases with depth. This is because the water at lower levels need to support the gravity of the water at higher levels. The water pressure increases uniformly by about 10,000 Pa/meter (or about 1 atmosphere /10 meter). Buoyant force in water comes from this pressure increase. The shape of the pipe does not affect the relation between pressure and depth.

Gravity and the motion of water Weight contributes to the net force on water. There are totally three forces on water. If there is no pressure imbalance, the water will fall. If the water pressure increases with depth by 10,000 Pa/meter, the water will not accelerate. If the pressure increase is more, the water will accelerate upward.

Siphon tube Demo: Siphon Water accelerates in the direction that lowers its total gravitational potential energy. To start the siphon, we need to prime the tube. There is a limit for the height of the tube we can use. It is about 10 m above the surface of the water . A pump at the bottom of the tube is more effective. Demo: Siphon

Bernoulli’s equation Water in a steady state flow along a single streamline has 1) pressure potential energy, 2) kinetic energy, and 3) gravitational potential energy. Water has a constant total energy per volume: Water can exchange energies through pressure, speed and height.

Examples of energy transformation-1 As water flows upward in a uniform pipe, Its speed can’t change (steady state flow in a uniform pipe). Its gravitational potential energy increases. Its pressure potential energy decreases.

Examples of energy transformation-2 As water falls downward from a spout, Its pressure stays constant, Its gravitational potential energy decreases. Its kinetic energy increases.

Examples of energy transformation-3 As a horizontal stream of water hits a wall, Its height is almost constant, Its kinetic energy decreases. Its pressure potential energy increases.

Read: Ch5: 2 Homework: Ch5: E27;P15 Due: November 10