Fluids - North Allegheny€¦ · 3Fluids.notebook 32 May 08, 2014 Bernoulli's Principle Daniel...
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3Fluids.notebook 1 May 08, 2014 Fluids mass volume density = ρ = m V
Transcript of Fluids - North Allegheny€¦ · 3Fluids.notebook 32 May 08, 2014 Bernoulli's Principle Daniel...
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Fluids mass volumedensity =
ρ = mV
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Pressureforce per unit area
P = FA
unit: N / m2 = Pascal (Pa)
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Fluid exerts a pressure in all directions.
Consider a tiny cube of water.
Pressure is the same on all sides of the cube. What if it wasn't?
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Force due to the fluid pressure always acts PERPENDICULAR
to the surface with which it is in contact.
What would happen if the water pushed on the glass at an angle, like this?
The glass would push back (actionreaction), and this reaction would cause the water to flow.
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Calculating Pressure at a Given Depth
take a point at a depth of "h" in a fluid
pressure there is due to weight of the column above it
so, F = mg =ρV =ρAhg
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Pascal's Principle
The pressure applied to a confined fluid increases the pressure throughout
by the same amount.
The Blob (scrub to 1:00)
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How can a person, with a realistic force,
stop a car?
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Buoyancyupward force exerted by a fluid on an object contacting the fluid
coin in water coin "in" mercury
As you can see, shape and density have something to do with buoyancy.
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How strong is the buoyant force (Fb)?
Fb = F2 F1= ρgAh2 - ρgAh1
= ρgA (h2 - h1)
= ρgV
= m g
Fb = Weight of fluid displaced
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Archimedes' Principle
(287? 212 BC)
The buoyant force on a body immersed in a fluid is equal to the weight of the
fluid displaced by the object.
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Fluid Dynamicsstudy of fluids in motion
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eddies
occurs when a fluid flows in parallel layers, with no disruption between the layers
Laminar Flow
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Fluid Dynamicsstudy of fluids in motion
eddies
occurs when a fluid flows in parallel layers, with no disruption between the layers
Laminar Flow
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Volume Flow Rate = Q = volume time
Q = = = A vA Δlt
Vt
Q = = A vVt
Take for example this reduced pipe:
rate of flow into pipe = rate of flow out of pipe
Why?mass of water into pipe = mass of water out of pipe (per unit of time) (per unit of time)
m1 m2t1 t2=
ρ1 V1 ρ2 V2t1 t2=
ρ1A1Δl1 ρ2A2Δl2 t1 t2
=
Q = = = A vA Δlt
Vt
ρ1A1v1 = ρ2A2v2
Equation of Continuity
when fluid is incompressible, ρ doesn't change
A1v1 = A2v2
special case of the Equation of Continuity
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Based on the equation of continuity, why does a hose shoot farther when you put your thumb over the end?
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ρ A v
ρ A v= same size areas
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Bernoulli's Principle
Daniel Bernoulli17001782Swiss
Beach Ball in Fan
Pingpong ball in faucet
Where the velocity of a fluid is high, the pressure is low, and
where the velocity of a fluid is low, the pressure is high.
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Bernoulli's Equation
W1 = F1 Δx1
= P1A1Δx1
W2 = F2 Δx2
= P2A2Δx2
There is also work done by gravity:
W3 = mg(y2 y1)
Wnet = W1 + W2 + W3
ΔKE = P1A1Δx1 P2A2Δx2 mg(y2 y1)
Consider the works done on the water flowing uphill in the pipe.
1/2 mv22 - 1/2 mv12 = P1A1Δx1 P2A2Δx2 mgy2 + mgy1
1/2 ρA2x2v22-1/2 ρA1x1v12 = P1A1Δx1 P2A2Δx2 ρA2x2gy2 + ρA1x1gy1
1/2 ρv22-1/2 ρv12 = P1 P2 ρgy2 + ρgy1
P1+1/2 ρv12 + ρgy1= P2 + 1/2 ρv22 +ρgy2
Bernoulli's Equation
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P1 = P2 and v2≈0b)
P1+1/2 ρv12 + ρgy1 = P2 + 1/2 ρv22 +ρgy2
1/2 v12 + gy1 = gy2
v1 = 2g(y2 y1)Torricelli's Theorem
(1608–1647)Evangelista Torricelli
Italian Student of Galileo
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