PhysicsPhysics 101:101: LectureLecture 1818 FluidsFluids IIII

Today’s lecture will cover Textbook Chapter 9

Physics 101: Lecture 18, Pg 1 ReviewReview StaticStatic FluidsFluids
Pressure is force exerted by molecules “bouncing” off container P = F/A

Gravity affects pressure

P = P 0 + ρgd

Archimedes’ principle: Buoyant force is “weight” of displaced fluid. F = ρ g V

Today include moving fluids!

A1v1 = A 2 v2 – continuity equation 2 2 P1+ρgy 1 + ½ ρv1 = P 2+ρgy 2 + ½ρv2 – Bernoulli’s equation

Physics 101: Lecture 18, Pg 2 08 ArchimedesArchimedes ’’ PrinciplePrinciple

Buoyant Force (F B) weight of fluid displaced

FB = ρfluid Vdisplaced g Fg = mg = ρobject Vobject g object sinks if ρobject > ρfluid object floats if ρobject < ρfluid

If object floats…

FB = F g Therefore: ρfluid g Vdispl. = ρobject g Vobject Therefore: Vdispl./ Vobject = ρobject / ρfluid

Physics 101: Lecture 18, Pg 3 10 PreflightPreflight 11 Suppose you float a large ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will: 1. Go up, causing the water to spill out of the glass. 2. Go down. 3. Stay the same.

Physics 101: Lecture 18, Pg 4 12 PreflightPreflight 22 Which weighs more: 1. A large bathtub filled to the brim with water. 2. A large bathtub filled to the brim with water with a battle-ship floating in it. 3. They will weigh the same. Tub of water + ship

Tub of water

Overflowed water

Physics 101: Lecture 18, Pg 5 15 ContinuityContinuity

A four-lane highway merges down to a two-lane highway. The officer in the police car observes 8 cars passing every second, at 30 mph. How many cars does the officer on the motorcycle observe passing every second? A) 4 B) 8 C) 16

How fast must the cars in the two-lane section be going? A) 15 mph B) 30 mph C) 60 mph Physics 101: Lecture 18, Pg 6 18 ContinuityContinuity ofof FluidFluid FlowFlow

• Watch “plug” of fluid moving through the narrow part of the tube (A 1) •Time for “plug” to pass point • Mass of fluid in “plug”

• Watch “plug” of fluid moving through the wide part of the tube (A 2) •Time for “plug” to pass point • Mass of fluid in “plug”

• Continuity Equation says m1 = m 2 fluid isn’t appearing or disappearing

Physics 101: Lecture 18, Pg 7 22 FaucetFaucet PreflightPreflight A stream of water gets narrower as it falls from a faucet (try it & see). Explain this phenomenon using the equation of continuity A1 V1

A2 V2

Physics 101: Lecture 18, Pg 8 23 FluidFluid FlowFlow ConceptsConcepts

ρ

A1 P1 v1 A2 P2 v2

• Mass flow rate: ρAv (kg/s) • Volume flow rate: Av (m 3/s)

• Continuity: ρA1 v1 = ρA2 v2 i.e., mass flow rate the same everywhere e.g., flow of river

Physics 101: Lecture 18, Pg 9 24 Pressure,Pressure, FlowFlow andand WorkWork

Continuity Equation says fluid speeds up going to smaller opening, slows down going to larger opening Recall: W=F d

Acceleration due to change in pressure. P 1 > P 2 = PA d = P V
Change in pressure does work! Venturi demo

Physics 101: Lecture 18, Pg 10 28 PressurePressure ACTACT

What will happen when I “blow” air between the two plates?

A) Move Apart B) Come Together C) Nothing

Physics 101: Lecture 18, Pg 11 31 BernoulliBernoulli ’’ss EqsEqs .. AndAnd WorkWork
Consider tube where both Area, height change.

W = ∆K + ∆U Note: 2 2 W=F d (P 1-P2) V = ½ m (v 2 – v1 ) + mg(y 2-y1) 2 2 = PA d (P 1-P2) V = ½ ρV (v 2 – v1 ) + ρVg(y 2-y1) = P V 2 2 P1+ρgy 1 + ½ ρv1 = P 2+ρgy 2 + ½ρv2

Physics 101: Lecture 18, Pg 12 34 BernoulliBernoulli ACTACT

Through which hole will the water come out fastest?

A

B

C

Physics 101: Lecture 18, Pg 13 37 ActAct A large bucket full of water has two drains. One is a hole in the side of the bucket at the bottom, and the other is a pipe coming out of the bucket near the top, which bent is downward such that the bottom of this pipe is even with the other hole, like in the picture below: Though which drain is the water spraying out with the highest speed? 1. The hole 2. The pipe 3. Same

Physics 101: Lecture 18, Pg 14 40 ExampleExample (like(like HW)HW) A garden hose w/ inner diameter 2 cm, carries water at 2.0 m/s. To spray your friend, you place your thumb over the nozzle giving an effective opening diameter of 0.5 cm. What is the speed of the water exiting the hose? What is the pressure difference between inside the hose and outside?

Physics 101: Lecture 18, Pg 15 LiftLift aa HouseHouse Calculate the net lift on a 15 m x 15 m house when a 30 m/s wind (1.29 kg/m 3) blows over the top.

Physics 101: Lecture 18, Pg 16 48 FluidFluid FlowFlow SummarySummary

ρ

A1 P1 v1 A2 P2 v2

• Mass flow rate: ρAv (kg/s) • Volume flow rate: Av (m 3/s)

• Continuity: ρA1 v1 = ρA2 v2 1 2 1 2 • Bernoulli: P1 + /2 ρv1 + ρgh 1 = P 2 + /2 ρv2 + ρgh 2

Physics 101: Lecture 18, Pg 17 50