bernoullisequation-101214045144-phpapp01

8/14/2019 bernoullisequation-101214045144-phpapp01

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The motion of Real fluids is verycomplicated and STILL not fully understood.So We will only analyze Ideal fluids.

In an Ideal fluid, the flow is

1. Stead y (or laminar ): The

velocity (speed and direction) ofthe fluid at any given point doesnot change. Example: smokefrom an extinguished candlechanges from laminar to turbulent.

laminar

turbulent


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2. Inc o m p ressib le: The fluids density isconstant.

3. Non visc ou s: An object movingthrough the fluid would experienceno viscous drag force (i.e. Onceset in motion, an object wouldcontinue at constant speedthrough a nonviscous )Viscosity is the fluid analog of

friction between solids, and thusis a measure of the fluidsresistance to flow.

Syrup and oilare highlyviscous fluids


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The flow of a fluid can be made visible byadding a t racer , such as a dye to a liquid flow or smoke to a gas flow. Each bit oftracer follows what is called a ___________.

Laminar flow in a liquidaround an obstacle

Airflow streamlines for acar in a wind-tunnel test.

streamline


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Mass of fluid entering tube in a given timemust equal mass of fluid exiting tube

21 mm

The Continuity Equation Conservation of Mass


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21 V V (V = Volume in this step)2211 X A X A

t v At v A 2211 (v = Velocity in this step)

2211 v Av A OR Constantv A

(Subs t i tu te

x = ..?)


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Constantv A is often called theVolume Flow Rate equation because the

term A v is equivalent to ___________, with SIunits of

As A , v __.

As velocityincreases,streamlines

_________.

An

Application:

Volume/time s

m3

get closer


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F 1 does positive workW 1 =

F 2 does negative work..W 2=

W net = W 1 W 2 =

____ 2211 X A X A

11111 x A P x F

22222 x A P x F

V V P V P 21

Bernoullis Equation Conservation of Energy


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The net work on the fluid, then, must equal the __________________ of the fluid.

Wnet =

change in energy

U K


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1. Fluids at Rest V 1 = V2 = ___

(Same result as derived earlier forstatic pressure!)

12 y y g gh

0


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2. Consider a pipe with multiple diameters,but at the same height

From Continuity Equation..

A1 V1 =

So the pressure of a moving fluid ________

as its speed increases!!

V2 A2

222

2

1 v P

1 P 2 P decreases


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Demonstrations

=We can make sense of this if we thinkabout F = ma Fluid speeds u p from 1 to 2, so the direction of the

net force on the fluid must be to the _______( __ > __ ).

Fluid s lo w s d o w n from 2 to 3, so the direction of thenet force on the fluid must be to the ______( __ < __ ).

rightP1 P2

leftP2 P3

=


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3. A large tank has a small pipenear the bottom. The speed at

which a fluid will escape outthe pipe can be calculatedusing Bernoullis Principle

Apply Bernoullis Equation between 1 and 2.

Since 1 is at the surface & 2 is just as thefluid leaves the tank, P 1 & P 2 are both ___absolute pressure or ___ gauge pressure(can use either in Bernoullis Equation, aslong as you are consistent!)

Pa0


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If the tank is large, V 1 ___

y = 0

Same result as for a bodythat _____________ from aheight, h.

Choosing a different 1 produces the same answer

choose point inside tank, a height, h, below the surface.

If the outlet pipe were redirected vertically, how highwould an ideal fluid rise above the outlet? ____!

0 2

21 v gh

ghv 22

ghv 2 free falls

2

21 v gh

h


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The purpose of the trap is to provide a barrier to preventsmelly sewer gases from entering the home. But what would

happen, then, if there was no vent?....When water from theclotheswasher would rush through the pipe, the high velocitywater would have a ________ pressure than atmospheric(Bernoulli). Since P B > P A, the water in the trap would bepushed out into the sewer line, allowing those nasty sewergases to enter your lovely home!!

lower

5. Household Plumbing What is the purpose ofthe U- shaped pipe beneath a sink called a (trap) ANDthe vent pipe that extends through the roof?


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The vent, then, ensures that the pressure on either sideof the water- filled trap is _________ (____________).So, when the clotheswasher empties its water to thesewer, water will NOT leave the trap.

Contrary to popular belief, the purpose of the vent isNOT to provide an escape route for the sewer gas!

the same atmospheric

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