Today Chapter 10 Fluids Review Concepts from Tuesday

Today (Chapter 10, Fluids) èReview Concepts from Tuesday èContinuity Equation èBernoulli’s Equation èApplications/Examples Tomorrow (Chapters 6 -10) èReview for Exam 2

Pressure When an object is submerged in a fluid (air, water, etc. ) it will feel a pressure from the fluid. This pressure is caused by the collision of molecules of the fluid with the surface of the object. From our own experience, we know that the pressure deeper in a fluid is more than the pressure at the surface. What is the difference in the pressure on the top of the object and on the bottom of the object?

Quiz Question! A submarine is constructed so that it can safely withstand a pressure of 1. 6 x 107 Pa. How deep can this submarine descend in the ocean if the average density of sea water is 1025 kg/m 3?

Fluids and Effect of Gravity • U-Tube Example 10. 3 on Page 316. • Consider a U-Tube with both ends open to the atmosphere. Let there be two liquids, water with density 1000 kg/m 3 and an oil with density 700 kg/m 3. Let the oil be filled 0. 10 m above the oil-water boundary. • Determine the difference in the level of the two liquids, d.

Pascal’s Principle (why hydraulics work) Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls. In other words, pressure applied at one end of a hydraulic system is added to every point in the system. F 1 A 1 F 2 A 2

Archimedes’ Principle Buoyancy (why things float) Any fluid applies a buoyant force to an object that is partially or completely immersed in it. The magnitude of the buoyant force equals the weight of the fluid that the object displaces. In other words, if the object can displace enough fluid, it will generate enough buoyant force to counteract it’s weight and it will float!

A solid block of wood that normally floats in water is pushed down and held under water by a physics 218 student. Does the water level in the container rise or fall? (rise) Before Is the buoyant force on the wood greater than, equal to, or less than the weight of the object? (greater) After

A flat-bottomed barge, loaded with coal, has a mass of 3× 105 kg. The barge is 20. 0 m long and 10. 0 m wide. It floats in the fresh water. What is the depth of the barge below the waterline?

A block of birch wood floats in oil with 90% of its volume submerged. What is the density of the oil? The density of the birch is 0. 67 g/cm 3.

Continuity Equation What comes in, must go out. Constant density

Continuity Equation What comes in, must go out. Mass flow rate Units: kg/s Volume flow rate Units: m 3/s

Continuity Equation (why a fire hose works) The mass flow rate has the same value at every position along a tube that has one entry point and one exit point. In other words, if you reduce the area that the fluid can flow through, it has to flow faster! What comes in, must go out. (If you shove 2 gallons of water in one end of a pipe in one second, 2 gallons of water must come out the other end of the pipe in one second. )

• Continuity Equation Example Water is flowing through a pipe with a cross-sectional area of 4. 0 cm 2 and connects to a faucet with an opening of area 0. 50 cm 2. If the water is flowing at a speed of 5. 0 m/s in the pipe, what is the speed as it leaves the faucet?

Bernoulli’s Equation (why a heavy airplane can fly) In a (steady, irrotational) flow of a (nonviscous, incompressible) fluid of density , the pressure, fluid speed, and elevation (y) at any two points are related by: In other words, if we are talking about two points with the same elevation: a quickly flowing fluid has a lower pressure than a slowly flowing fluid.

Application: Bernoulli’s Equation • What is the upward “lift” force on an airplane wing? • • • Assume the area of the wing is 60 m 2 The speed of air over the wing is 250 m/s The speed of air under the wing is 200 m/s Let the wing be 1 meter thick Assume the density of the air to be 1. 29 kg/m 3

Difference in Pressures • The pressure in the atmosphere is not a constant, but fluctuates as the weather changes. • Consider a window of a house where the pressure inside is 101, 000 Pa and the pressure outside has decreased to 96000 Pa. Let the area of the window be 1. 5 m 2. • What is the force exerted on the window due to this difference in pressures?

Fluids and Gravity A new water tower is built on a very tall hill. At a nearby house, the pipes are leaking because the pressure in the water is too high. Assume water pipes leak when the pressure exceeds five times atmospheric pressure. Determine the relative height of the water tower in comparison to the house.

Archimedes’s Principle and Buoyancy • Consider a wooden block of density 700 kg/m 3 and a volume of 2. 0 m 3. • Determine the force required to hold it completely under water.

Archimedes’s Principle and Buoyancy • Concept: Apparent Weight • Consider a piece of aluminum attached to a string and suspended in a pool of oil (density 750 kg/m 3). • Let the apparent weight of the aluminum be 540 N. • Determine the volume of the aluminum.