Question

The rate of flow `Q` (volume of liquid flowing per unit time) through a pipe depends on radius `r`, length `L` of pipe, pressure difference `p` across the ends of pipe and coefficient of viscosity of liquid `eta` as `Q prop r^(a) p^(b) eta^(c ) L^(d)`, then
A. `a = 4, b = 1, c = - 1, d = -1`
B. `a = 4, b = -1, c = 1, d = -1`
C. `a = 4, b = 1, c = 1, d = -1`
D. values of a,b,c ang d cannot be detemind

Answer 1

Correct Answer - D
(4) `Q prop r^(a) p^(b) eta^(c ) L^(d)`
`L^(3) T^(-1) prop [L]^(a) [ML^(-1) T^(-2)] [ML^(-1) T^(-1)]^(c ) [L]^(d)`

`M^(0) L^(3) T^(-1) prop M^(b + c) L^(a- b - c + d) T^(- 2b - c)`
`b = c = 0, a - b - c + d = 3, - 2b - c = -1`
Three equaitons, four unknowns,