How Can I Solve This Fluid Dynamics Homework Problem?

[Adam Rabe]

Homework Statement

Homework Equations

AV = AV
P + 1/2*p*v^2 + pgh = P + 1/2*p*v^2 + pgh

The Attempt at a Solution

For a.) ... divide 3 by 0.1 because of (AV = AV) = 30 ms-1. answer is right.
For b.) I am stuck on this one. I tried using the 2nd relevant equation above but i can't seem to find the answer and I am sure i need to use that one. Heres my working out.

Pressure A: P + (0.5 *1000 *3^2) = 5 *10^5... Therefore P = 495500 Pa
Pressure B: P = 495500 + (0.5 *1000 *30^2) + (1000 *10 *1) = 955500 Pa
Answer is 6.5 *10^4... (65000)

For c.) point is located at the same height and same area as A, therefore pressures are equal = 5 * 10^5 Pa. Answer is right

Any help would be greatly appreciated. Thanks in advance
Adam

 

[haruspex]

Pressure A: P + (0.5 *1000 *3^2) = 5 *10^5... Therefore P = 495500 Pa

You don't seem to understand the Bernoulli equation. P is the pressure at the given point. At A it is 5*10^5 Pa. The other terms are then added to this to get a quantity that is the same throughout the streamline.

 

[Adam Rabe]

You don't seem to understand the Bernoulli equation. P is the pressure at the given point. At A it is 5*10^5 Pa. The other terms are then added to this to get a quantity that is the same throughout the streamline.

Hello sorry for the late reply.
i think i see where i went wrong...
Using your advice, i added the pressure change due to height and subtracted the pressure difference between the two speeds (as fluid speeds up pressure must drop)

5*10^5 + (1000 *10) - ((0.5 * 1000 * 30^2) - (0.5 * 1000 * 3^2)) = 64500

But I am still 500 Pa off from the right answer, am i on the right track?

 

[haruspex]

64500

That's what I get. Looks like the answers have been rounded to 2 significant figures.
The question statement is poor. It gives values like "1m²", "5x10⁵Pa". Standard interpretation says these are only accurate to one decimal place. If you follow that through the calculation you find that the answer is indeterminate. E.g. just change the 3m/s to 3.1m/s and you get a much smaller answer. It should quote the values as 3.00m/s etc. to justify 2 sig figs in the answer.