Question

the cross sectional areas of the main pipe and the constriction are 0.139 m2 and 0.0464 m2, respectively, and the pressure difference between the two portions is 55.2 kPa the velocity of flow in the main pipe is

a. .305 m/s

b. 1.73 m/s

c. 3.66 m/s

d. 11.0 m/s

e. 20.7 m/s

Answer 1

V1A1 = V2A2

V1 ( 0.139 m2 ) = V2 ( 0.0464 m2, )

V1= 0.338 V2 apprx

P1 + 0.5 $\rho$ v1^2 = P2 + 0.5 $\rho$ v2^2

P1- P2 = 0.5 (1000)( v2^2 - v1^2)

55.2 x 10^3 = 0.5 (1000)(V2 ^2 - 0.338 V2^2)

110.4 = 0.88556 v^2

v^2 = 110.4 / 0.88556

v2 = 11.165 m/s

v1 = 3.77 m/s apprx