(a) Find the speed of flow in the lower section. . m/s (b) Find the speed of flo

Question

(a) Find the speed of flow in the lower section.
. m/s

(b) Find the speed of flow in the upper section.
m/s

(c) Find the volume flow rate through the pipe.
m3/s

Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is 1.70 (a) Find the speed of flow in the lower section. . m/s (b) Find the speed of flow in the upper section. m/s (c) Find the volume flow rate through the pipe. m^3/s x 10^5 Pa and the pipe radius is 1.20 cm. x 10^5 Pa and the pipe radius is 2.50 cm. At the higher point located at y = 2.50 m, the pressure is 1.25

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 = 2.1*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*(2.1^2*v1^2-v1^2) = (P1-P2) - rho*g*y

0.5*rho*(2.1^2-1)*v1^2 = (P1-P2) - rho*g*y

0.5*1000*3.41*v1^2 = (1.7e5-1.25e5)-(1000*9.8*2.5)

v1 = 3.47 m/s

v2 = 2.1*v1 = 7.287 m/s

flow rate = A1*v1 = 3.14*2.5*2.5e-4*3.47 = 6.81 m^3/s

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