Water moves through a constricted pipe In steady, ideal flow. At the lower point

Question

Water moves through a constricted pipe In steady, ideal flow. At the lower point shown n the figure below, the pressure is 1.70 x 10^5 Pa and the pipe radius s 2.90 cm. At the higher point located at y = 2.50 m, the pressure Is 1.24 x 10^5 Pa and the pipe radius Is 1.20 cm. (a) Find the speed of flow in the lower section. X Your response is within 10% of the correct value. This may be due to round off error, or you could have a mistake in your calculation. Carry Out all intermediate results to at least four-digit accuracy to minimize round off error. m/s (b) Find the speed of flow in the upper section. 6.554 m/s (c) Find the volume flow rate through the pipe. Your response is off by a multiple of ten. m^3/s

Explanation / Answer

continuity equation

A1*v1 = A2*v2

pi*r1^2*v1 = pi*r2^2*v2

r1^2*v1 = r2^2*v2

v2 = (r1/r2)^2*v1 = 5.84*v1

bernoullis pricilple

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

(P1-P2) - rho*g*y = 0.5*rho*(v2^2-v1^2)

0.5*rho*(v2^2-v1^2) = (P1-P2) - rho*g*y

0.5*rho*(5.84^2*v1^2-v1^2) = (P1-P2) - rho*g*y

0.5*rho*(5.84^2-1)*v1^2 = (P1-P2) - rho*g*y

0.5*1000*33.1056*v1^2 = (1.7e5-1.24e5)-(1000*9.8*2.5)

#a) v1 = 1.139 m/s

#b) v2 = 5.84*v1 = 6.65176 m/s

#c)

flow rate = A1*v1 = 3.14*2.9*2.9*1e-4*1.139 = 3*10^-3 m^3/s

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