Bernoullis-Relating things with height

[September24]

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Usually, bernoullis talks about Pressure and velocity being inversely related.

Do P and velocity go down as height increases?

I took a kaplan test and they stated that as elevation increases (height goes up), velocity should stay the same. I understand that Pressure decreases as height increases but what is pressure was consistent somehow, would velocity decrease?

 

[FeinMS]

Velocity also depends on area. A1V1=A2V2. If the elevation increases without changing the area of the pipe, the velocity stays the same. In P+0.5(rho)(V^2)+(rho)(g)(h)=C, the third term increases and second term stays the same, so the first term must decrease.

 

[jtran7]

if you are referring to bernoulli hes dealing with fluid pressure so when you increase the height (depth) below the water surface the pressure increases.

and if you are talking about velocity I imagine 2 situations

the first is where a big tanker of water has a outlet pipe and you are trying to find the velocity of fluid leaving the pipe

so you would use his equation:

P1 + 1/2 roe V1^2 + roe * g * h = P2 + 1/2 roe V2^2 + roe * g * H2

- assuming the pipe opens to the atmosphere P1 and P2 would be equal so they cancel out.
- H1 is at the surface of the water level in the tanker so it is zero, while H2 is the depth of the pipe from the surface

so the equation becomes...

1/2 roe V1^2 = 1/2 roe V2^2 + roe* g* H2

then since the tanker is so much larger than the pipe V1 (the speed at which the tanker water height changes) is close to zero

so the equation becomes...

V2 = squareroot of 2*g*H2

in this situation as you increase depth you increase pressure resulting in increase velocity out of the pipe (intuitively if there is greater pressure on one side the flow will flow out faster)


The other situation is that of fluid flow thru a pipe at the same height but different section with different area...

in this situation using his equation again

P1 + 1/2 roe V1^2 + roe * g * h = P2 + 1/2 roe V2^2 + roe * g * H2

we cancel out the H1 and H2 because they will be the same so the equation becomes....

P1 + 1/2 roe V1^2 = P2 + 1/2 roe V2^2

now if the pipe area is large then turns small, using A1V1 = A2V2 we know that the larger section will have fluid velocity that is slower and the smaller section of the pipe will have a faster fluid velocity

then by using the previous equation...

P1 + 1/2 roe V1^2 = P2 + 1/2 roe V2^2

we know that V1 < V2 therefore P1 > P2