Power P is a function of

1) Head, H 2) Discharge, Q

3) Specific weight, w

P= KH$^{a} . Q^{b}.. w^{c}$

where K= non- dimensional constant

substituting the dimensions on both sides of equation 1)

ML$^{2}T^{-3}=KL^{a}.(L^{3}T^{-1})^{b}.(ML^{-2}T^{-2})^{c}$

equating the power M,L and T on both sides

Power of m, 1=c c=1

Power of L, 2=a+3b-2c a=2-3b+2c = 2-3+2=1

Power of T, -3= -b-2c

b=3-2c

=3-2=1

substituting the values of a,b,c in P=KH$^{\prime}.q^{\prime}.w^{\prime}$

=KHQW