Water flows out of a large reservoir through 5-cm diameter pipe. The pipe connec

Question

Water flows out of a large reservoir through 5-cm diameter pipe. The pipe connects to a
3-cm diameter pipe that is open to the atmosphere, as shown in Fig. 13-7. What is the
speed of the water in the 5-cm pipe?

I know I have to use Bernoulli's equation but I really have no idea where to start with this. Please help me!

Water flows out of a large reservoir through 5-cm diameter pipe. The pipe connects to a 3-cm diameter pipe that is open to the atmosphere, as shown in Fig. 13-7. What is the speed of the water in the 5-cm pipe?

Explanation / Answer

P1 + rho*g*h1 + 0.5*rho*v1^2 = P2 + rho*g*h2 + 0.5*rho*v2^2


here P1 = P1 = atmospheric pressure and v1 = 0

so,

0.5*rho*v2^2 = rho*g*(h1-h2)


let v2 = v and h1-h2 = h


0.5*v^2 = g*h

v = sqrt(2*g*h)


v = sqrt(2*g*h) = sqrt(2*9.8*4) = 8.854 m/s


let d1 = 5cm, v1 = ?

d2 = 3 cm , v2 = 8.854 m/s

A1*v1 = A2*v2

V1 = (A2/A1)*v2

V1 = (d2^2/d1^2)*v2

= (9/25)*8.854

= 3.19 m/s

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