Hydrodynamics

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cipker

2009-07-23 6:05 am

Water flows into a tank of large cross-sectional area at a rate of 10^(-4) m^3/s, but flows out from a hole of area 100mm^2, which has been punched through the base. How high does the water rise in the tank?

A. 20mm
B. 22.36mm
C. 25mm
D. 50mm
E. 100mm

Which is correct?

更新1:

Isn't that A1v1 = A2v2 (law of continunity) v2 = A1v1/A2 = (10^-4)v1/(100 x 10^-6) Why v2 = 10^-4 / 100 x 10^-6 ? Also, why v2² - v1² = v2² ?

回答 (1)

Prof. Physics

2009-07-23 1:41 pm

✔ 最佳答案

Let p be the density of water.

Water velocity, v2 = 10-4 / 100 X 10-6 = 1 ms-1

By Bernoulli's principle,

P0 + 1/2 pv12 + pgh1 = P0 + 1/2 pv22 + pgh2

pg(h1 - h2) = 1/2 p(v22 - v12)

Rise in height, h1 - h2 = (1)2 / 2g

= 1 / 2(10)

= 0.05 m

= 50 mm

The answer is D.

參考: Physics king

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