Name: Knowunity
Brand: Knowunity

English (US)

Notes regarding derivation of the Bernoulli's equation and how it is used.

https://content-eu-central-1.knowunity.com/CONTENT/dxVOCMAmzveqLITDkBSZ.pdf

AP Physic 2 - 1

Study note

United States of America

DEFAULT (US)

AP Physics 1

AP Physic 2 - 1.6

Simple Harmonic Motion and Rotational Motion

Density and Pressure

Unit 1 Fluids:
1.6 Bernoulli's Equation -
*Using Conservation of Energy
- Bernoulli's Equation is derived from applying conservation of energy to the flow
of an ideal fluid:
Derivation Shown Below:
The change in kinetic energy is: AK = mv2-mv²
The change in potential energy is: AU = mgy₂-mgy₁
The work energy relationship is then:
P₁V-P₂V=1
1
mv²
mví +mgy2-mgy1
Since p = mV, dividing the entire equation by volume yields:
1
1
P₁-P₂ = pv²-pv² + pgY2 − pgy₁
1
1
→ P₁ + pv² + pgy₁ = P₂ + pv² + pgy2
1
==mv²/₁
Going back to Physics 1, the change in energy is due to work done by outside
forces. The work done on the fluid from the outside forces exerting pressure is
equal to the total change in energy: Wnet = AK + AU
• The work done on each end of the fluid flow is: W=FAx=(PA)Ax=PV
Fluid velocity is low where pressure is high and fluid velocity is high where
pressure is low.
The essential equation is this:
1
1
P₁ + pgh₁ + ₂pv₁ = P₂ + pgh₂ + pv²
A typical usage of this equation will be any problem like ●
O
V, P.
■
Bernoulli's Equation
h,
P₁+ pv² + pgh₁ = P₂ + pv² + pgh₂
A, A, Cross-sectional areas at points 1 and 2
PP, Pressures
VV Velocities
hh,
Elevations
Source: Science's Fact
P₂
1
Important things to note:
o Always set the lower portion height as 0. That will be your reference point to
where height is 0. And the other will be a positive number if there is an increase
in height.
Area is typically calculated via the formula of a circle. A question will give you the
radius or diameter and you have to calculate the area.
o If you subtract any of these quantities into a (Final - Initial) format using algebra
that is the change of that quantity.
P2P1 = change of pressure and then you can solve the problem for
that quantity.
Batt

AP Physic 2 - 1.6

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

20 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying

AP Physic 2 - 1.6

Sign up to see the content. It's free!

Sign up to see the content. It's free!

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

20 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying