Q1: To replace a pipe of diameter D by n parallel pipes of diameter d, the formula is

ANS:D -

Here discharge through Pipe of dia 'D'= Q.
Discharge through one pipe of dia 'd'= q.
So, Total discharge through 'n' no. Of pipes od dia 'd' = n*q
Now if we replace the big dia pipe by small dia pipe then discharge has to be same
Q=nq.

Squaring both sides
Q^2=n^2.q^2 ----------> (1)
Put the value of Q^2 and q^2 by using formulae.
H=(flQ^2)/(12*D^5)
Value of f, l and h will be same for both pipes for the same discharge.
So, eqn 1 becomes;
D^5 = n^2*d^5.
d = D/n^(2/5).