fluid dynamics

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Fluid Dynamics Two Parts 1.Fluid Flow 2.Bernoulli’s Equation and Applications

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Fluid Dynamics. Two Parts Fluid Flow Bernoulli’s Equation and Applications. Assumptions for Fluid Flow:. Non-viscous. (isn’t “sticky”) I ncompressible (constant ρ ) All particles in cross section travel at the same speed (flow rate) Flow is laminar (no turbulence). Streamline flow. - PowerPoint PPT Presentation

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Page 1: Fluid Dynamics

Fluid DynamicsTwo Parts1. Fluid Flow2. Bernoulli’s Equation and Applications

Page 2: Fluid Dynamics

Assumptions for Fluid Flow:

Streamline flow Turbulent flow

1. Non-viscous. (isn’t “sticky”)

2. Incompressible (constant ρ)

3. All particles in cross section travel at the same speed (flow rate)

4. Flow is laminar (no turbulence)

Page 3: Fluid Dynamics

Laminar FlowLaminar flow, type of fluid (gas or liquid) flow in which the fluid travels smoothly or in regular pathsLaminar flow over a horizontal surface may be thought of as consisting of thin layers, or laminae, all parallel to each other.

Page 4: Fluid Dynamics

Laminar Flow• Video:

Page 5: Fluid Dynamics

Flow RateFlow Rate (ƒ): Volume of fluid that passes a particular point in a given timeUnits used to measure Flow Rate = m³/secEquation for: Flow Rate

ƒ = Aν = (m2)(m/s)

(A = cross sectional area)(ν = velocity of fluid)

Page 6: Fluid Dynamics

Rate of Flow

V Avt

AvtR vAt

Rate of flow = velocity x area

vt

Volume = A(vt)

A

Page 7: Fluid Dynamics

Since A1 > A2…

1 1 2 2R v A v A

For an incompressible, frictionless fluid, the velocity increases when the cross-section decreases:

Page 8: Fluid Dynamics

Continuity EquationFlow rates are the same at all points along a closed pipeContinuity Equation:

ƒ₁ = ƒ₂A₁ν₁ = A₂ν₂

Reminder: the equation for Area of a circle: A = πr²

Page 9: Fluid Dynamics

PHet• Fluid Flow

Page 10: Fluid Dynamics

Question:Water travels through a 9.6 cm diameter fire hose with a speed of 1.3 m/s. At the end of the hose, the water flows out through a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle?

Page 11: Fluid Dynamics

Venturi Meter

The higher the velocity in the constriction at Region-2, the lower the pressure... Wait what?

Page 12: Fluid Dynamics

Venturi Effect

Page 13: Fluid Dynamics

Venturi Effect

Page 14: Fluid Dynamics

Airplane Wings

Page 15: Fluid Dynamics

Airplane Wings

Page 16: Fluid Dynamics

How do Plane’s FlyVideo

Page 18: Fluid Dynamics

QuestionA small ranger vehicle has a soft, ragtop roof. When the car is at rest the roof is flat. When the car is cruising at highway speeds with its windows rolled up, does the roof a. bow upward b. remain flatc. bow downward?

Page 19: Fluid Dynamics

QuestionA small ranger vehicle has a soft, ragtop roof. When the car is at rest the roof is flat. When the car is cruising at highway speeds with its windows rolled up, does the roof a. bow upward b. remain flatc. bow downward?

Page 20: Fluid Dynamics

Fluid Flow Questions1. MC - 4,14,21,42,47 2. Homework: Watch Bernoulli Video3. MOST IMPORTANTLY: Paper Airplane Competition next classGo to: http://www.funpaperairplanes.com/index.html

a. Pick a plane and build it for the start of classb. Make TWO of the same designc. Planes will be thrown in players halld. Winner will be determined by displacement from initial throw

Page 21: Fluid Dynamics

Sports Science• Record Paper Airplane

Page 22: Fluid Dynamics

Conservation of Energy of Fluids within a Pipe

Bernoulli's PrinciplePRESSURE plus ENERGY is CONSTANT!1. P + E = P + E2. P + U + K = P + U + K3. P + ρgh + ½ρν² = P + ρgh + ½ρν²This hold at ANY point!

P1 + ρgh1 + ½ρν1² = P2 + ρgh2 + ½ρν2²

Page 23: Fluid Dynamics

Bernuolli Effect1. High Velocity: _____ Pressure2. Low Velocity: _____ Pressure

Page 24: Fluid Dynamics

Bernuolli Effect1. High Velocity: LOW Pressure2. Low Velocity: HIGH Pressure

Page 25: Fluid Dynamics

Special Case #1 – Horizontal Pipe2 2

1 1 1 2 2 2½ ½P gh v P gh v

Horizontal Pipe (h1 = h2)

2 22 1½ ½P gh v v Horizontal Pipe

Page 26: Fluid Dynamics

QuestionSuppose the pressure in the fire hose is 350 kPa. What is the pressure in the nozzle? ν1 = 1.3 m/sν2 = 19.17 m/s

Page 27: Fluid Dynamics

Special Case #2 – Constant Velocity2 2

1 1 1 2 2 2½ ½P gh v P gh v

Constant velocity (ν1 = ν2)

Notice how a difficult problem becomes easier when we remove constants!

Page 28: Fluid Dynamics

QuestionWater flows with constant speed through a garden hose that goes up a step 20.0 cm high. If the water pressure is 143 kPa at the bottom of the step, what is its pressure at the top of the step?

ν1 = ν2

Page 29: Fluid Dynamics

Special Case #3 – Fluids at Rest2 2

1 1 1 2 2 2½ ½P gh v P gh v

P1 - P2 = gh2 - gh1 P = g(h2 - h1)

We have already seen this!

Page 30: Fluid Dynamics

Special Case #4 – No Change in PressureKnow as Torricelli’s Theorem

2 21 1 1 2 2 2½ ½P gh v P gh v

2v gh

h1

h2h

Torricelli’s theorem:

2v gh

v2 0

Page 31: Fluid Dynamics

Question:A dam springs a leak at a point 20.0 m below the surface. What is the emergent velocity?

2v ghh

v = 19.8 m/s2

Page 32: Fluid Dynamics

Summary of Hydrodynamics

1 1 2 2R v A v A Streamline Fluid Flow in Pipe:

PA - PB = ghHorizontal Pipe (h1 = h2)

2 21 2 2 1½ ½P P v v

Fluid at Rest:

Bernoulli’s Theorem:2

1 1 1½P gh v Constant

Torricelli’s theorem:

2v gh

Page 33: Fluid Dynamics

Bernoulli’s Principal1. MC: 5,13,22,25,27,28,33,36,37,44 2. Homework: Review Free Response Questions Posted

on Website3. Next Class: Hydrodynamics Quiz