Chapter 8 2 St Augustine Preparatory School February

Chapter 8 -2 St. Augustine Preparatory School February 17, 2016

Pressure • Pressure is a measure of how much force is applied over a given area. • The formula for pressure is: Term Unit/Symbol Pressure (P) Pascal (Pa) Force (F) Newton (N) Area (A) Meters squared (m 2)

Pressure • When you pump up a soccer ball, every section on the inside wall of the soccer ball feels the exact same pressure. • Pascal’s Principle: Pressure applied to a fluid in a closed container is transmitted equally to every point on the fluid and to the walls of the container. • This principle is evident in hydraulic lifts

Formula for situations with two different areas, such as lifts: P 1 = P 2 so: • In the hydraulic lift to the left, the pressure will be the same at every single point in the lift. Remember, P=F/A, so by applying a force at F 1, pressure is increased everywhere in the system. Since the area (A 2) does not decrease, this means the force must increase.

Sample Problem • The small piston of a hydraulic life has an area of 0. 20 m 2. A car weighing 1. 20 x 104 N sits on a rack mounted on the large piston. The large piston has an area of 0. 90 m 2. How large a force must be applied to the small piston to support the car.

Solution A 1 = 0. 20 m 2 and F 1 = ? A 2 = 0. 90 m 2 and F 2 = 1. 20 x 104 N

Problem 2 • In a car lift, compressed air exerts a force on a piston with a radius of 5. 00 cm. The pressure is transmitted to a second piston with a radius of 15. 0 cm. a. How large a force must the compressed air exert to lift a 1. 33 x 104 N car? b. What pressure produces this force? Neglect (ignore) the weight of the pistons.

Solution Part a Part b

Pressure varies with depth • The deeper into a fluid an object goes, the more pressure it experiences. • In the ocean, water pressure increases with depth because the water at a given depth must support the weight of the water above it. • At the top of a mountain, the pressure is less than at the bottom. This is because there are fewer air molecules at the top than at the bottom.

Atmospheric, Absolute, and Gauge Pressure • Absolute pressure is the total amount of pressure present. It is zero-referenced against a perfect vacuum. • Gauge pressure is the amount of pressure over and above the atmospheric pressure. • Atmospheric pressure is the pressure from the force exerted by the weight of the air around us. • So: Absolute = atmospheric + gauge

Fluid Pressure as a Function of Depth Formula: P = Po + ρgh Absolute pressure = atmospheric pressure + (density x gravity acceleration x depth) This formula can help explain buoyancy. Since the bottom of the box is further into the fluid, the pressure on the box is greater (since h will be greater). Recall, pressure = force / area. If pressure Increases, and area doesn’t change, then the force must increase.

Example Problem • How deep must the top of an object be in the a fresh water lake to have an absolute pressure three times the amount of the current atmospheric pressure of 100. 1 k. Pa. Assume the density of the fresh water is that of pure water: 1000 kg/m 3.

Solution Convert 100. 1 k. Pa to Pa: 100. 1 k. Pa * (1000 Pa/1 k. Pa) =100, 100 Pa P = Po + ρgh 3(100, 100 Pa) = (100, 100 Pa) + (1000 kg/m 3)(9. 81 m/s 2)h 200, 200 Pa = (1000 kg/m 3)(9. 81 m/s 2)h 200. 2 = (9. 81 m/s 2)h 20. 4 m = h

Practice Problems Page 288 #10 – 16 **The second part of question 11 wants to know how you can express the unit of pressure in terms of other units. For example: What is the SI unit of Force? What is it equal to, in other terms of other SI units. The SI unit of Force is Newton’s. F = ma = kg*m/s 2 , so a Newton can be expressed as a kg*m/s 2