Chapter 8 BHydraulics and Fluid Flow Pascals Principle

Chapter 8 BHydraulics and Fluid Flow

Pascal’s Principle • Famous scientist named Blaise Pascal • • Experimented with water Learned that: changes of pressure on the surface of a confined fluid are exerted equally throughout the fluid and at all points on the fluid’s container • Pascal’s Principle • But… what does that mean?

Pascal’s Principle Hydraulic system

P 1 = P 2 P 1 P 2 Amount of work done in the left piston is equal to the right piston So, if you apply a small force on the small piston and get a larger force on the large piston.

Example: A downward force of 100 N is applied to the small piston with a diameter of 50 cm in the hydraulic system. a) What is the upward force exerted by the large piston with a diameter of 2 m? P 1 = P 2 P 1 P 2

Pascal’s Principle • But to work: • Fluid must be confined in a closed container • Fluid must be incompressible • Cannot be squeezed • This means- liquids only! • Gases are too compressible

Simple Hydraulic Machines •

Example: A downward force of 100 N is applied to the small piston with a diameter of 50 cm in the hydraulic system. b) What is the mechanical advantage of this hydraulic lift? P 1 = P 2 P 1 • Whatever work/force is being applied, the output will be 16 times larger P 2

Example: A downward force of 100 N is applied to the small piston with a diameter of 50 cm in the hydraulic system. c) If the input force of 100 N pushes the small piston down by 2 m, how high will the large piston rise? P 1 = P 2 P 1 The machine didn’t multiply the input force (F 1) for nothing. We had to apply small force for a longer distance. (Distance principle) P 2

Example 2: A 1500 kg car is placed on the large piston with a radius of 4 m. a) What is the minimum upward force that the large piston must exert to lift the car? b) If the mechanical advantage of the hydraulic lift system is 20, what is the minimum downward force that should be applied to life the car? d) What is the pressure exerted by the large piston? e) How far should the small piston descend in order to lift the car by 2 m? P 1 = P 2

Flowing Fluids • What do fluids do? • Flow • But… what makes them flow? • Pressure • • Closed faucet= closed system Open faucet= open system (low pressure at opening), so water has to move to distribute pressure equally EVERYWHERE

Flowing Fluids • Weather System Pressure • Air (wind) blows from high-pressure to low pressure

Bernoulli’s Principle • Bernoulli (famous scientist) studied flow of water • • Looked at size and shape of pipes Water pressure is related to water’s height in the pipe and it’s velocity

Bernoulli’s Principle • Simple equation: • P 1+KE 1+PE 1 = P 2+KE 2+PE 2 • Bernoulli’s Principle • Total energy (kinetic energy + potential energy + pressure) for a confined ideal fluid flowing through a pipe is conserved at all locations within the pipe

Bernoulli’s Principle Bernoulli's principle: At points along a horizontal streamline, higher pressure regions have lower fluid speed and lower pressure regions have higher fluid speed.

Bernoulli’s Principle Bernoulli's principle: At points along a horizontal streamline, higher pressure regions have lower fluid speed and lower pressure regions have higher fluid speed.

The Coanda Effect

The Coanda Effect • Coanda effect- tendency of fluid flowing past a curved surface follows the surface

The Coanda Effect • Lift (supporting force) on airplane wing is because of the pressure difference between top of the wing and bottom