Question

A 30 cm pipe divides into a 24 cm branch A and a 15 cm branch B. If the total discharge is 0.26 m/s and if the same mean velocity occurs in each branch, what is the discharge in (a) branch A and (b) branch B? (a) Q24 cm = m /s (b) Q15 cm = m/s

Answer 1

Solution:

Q1 = A V Q = AV - Q2 = AzV2

Q=Q1 + O2

Q= A1V1 + A2V2

Given that the mean velocity in each branch is same i.e.

Vi= 1

Q = AV1 + A2V1 = (A1 + A2 V1

X 0.242 A1 = - = 0.045238934 m?

42 = TX 0.154 -= 0.017671458 m2

Q= (A1 + A2)

0.26 m/s = (0.045238934 m+ 0.017671458 m2)

V1 = 4.132862442 m/s

(a) Discharge in 24 cm pipe

Q1 = 24 cm = A1V1

Q24 cm = 0.045238934 x 4.132862442 m /s

$\framebox{Q_{24\ cm}=0.186966292\ m^3/s}\ \ \ Answer$

(b) Discharge in 15 cm pipe

Q2 = Q 15 cm = A2V1

$Q_{15\ cm}=0.017671458\times 4.132862442\ m^3/s$

$\framebox{Q_{15\ cm}=0.073033707\ m^3/s}\ \ \ \ Answer$