Please help me solve this fluid mechanics question!! >O<?

blue01

2009-06-11 9:35 pm

What is the pressure drop due to the Bernoulli effect as water goes into a 3cm diameter nozzle from a 9 cm diameter fire hose while carrying a flow of 5x10^-4m^3/s?

回答 (1)

[匿名]

2009-06-12 1:00 am

✔ 最佳答案

http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

P1 + 0.5*rho*V1^2 + rho*g*h1 = P2 + 0.5*rho*V2^2 + rho*g*h2

We assume there is no change in elevation between the hose and the nozzle===> rho*g*h term drops out

We need velocities at the hose(1) and nozzle(2)

Flow Rate = velocity * cross-section

0.0005 m^^3/s = V1 *(pi*r1^2)
0.0005 = V1 *(pi * (4.5 *10^-2)^2)

V1 = 0.0005 / 0.0063 = 0.08 m/s

0.0005 = V2 * (pi *0.015^2)

V2 = 0.0005 / 0.00071 = 0.71 m/s

P1 + 0.5*rho*0.08^2 = P2 + 0.5*rho* 0.71^2

P1 - P2 = 3.2 * 10^-3 - 0.25

P1 - P2 = 0.0032 - 0.25 = - 0.2468 Pa

Check my math and units.

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