Question 1.4: pump discharges liquid at the rate of Q against a head of H.......

Let Power P be given by:
P = f(w, Q, H) = kw^aQ^bH^c
where k, a, b, and c are constants. Substituting the respective dimensions in the above equation,
ML^2T^{-3} = k(ML^{-2}T^{-2})^a(L^3T^{-1})^b(L)^c
Equating corresponding indices, for M, 1 = a or a = 1; for L, 2 = -2a + 3b + c; and for T, -3 = -2a – b or b = 1, so c = 1.

Therefore,
P = kwQH