physic

2006-11-22 1:15 pm
Show that Bernoulli's equation reduces to the hydrostatic variation of pressure with depth (Eq. 10-3b) when there is no flow (v1 = v2 = 0). (Do this on paper. Your instructor may ask you to turn in this work.)

Equation 10-3b
change P=pgh2-h1

回答 (1)

2006-11-22 4:44 pm
✔ 最佳答案
Hydrostatic equation: dP/dz = -pg, where P=pressure, z=depth, p=rho=density, g=gravitational acceleration.

Bernoulli equation: P + pgh +.5*pv^2 = constant.
We have P1, z1 (depth), and v1=0; P2, z2, and v2=0.

So P1 + pgz1 = P2 +pgz2.
P1 - P2 = pg(z2-z1)
-dP = pg dz
So dP/dz = -pg. This is the hydrostatic variation of pressure. Pressure changes depends on g and density only.

You can write it as equation 10-3b. It's the same thing. Note that there is a negative sign in my answer, while the equation on says 'change in P'.

Hope this helps.
參考: I'm a 0.5 hydrologist + my physics text.


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