A horizontal tube has different cross sections at points `A` and `B`. The areas of cross section are `a_(1)` and `a_(2)` respectively, and pressures at these points are `p_(1)=rhogh_(1)` and `p_(2)=rhogh_(2)` where `rho` is the density of liquid flowing in the tube and `h_(1)` and `h_(2)` are heights of liquid columns in vertical tubes connected at `A` and `B`. If `h_(1)-h_(2)=h`, then the flow rate of the liquid in the horizontal tube is

Options

A. ` a _ 1 a_2sqrt ((2gh)/(a_1^2 - a _2^2 ) ) `
B. ` a _ 1 a_2 sqrt ( (2g)/(h(a_1^2 -a _ 2 ^2))) `
C. ` a_1a_2 sqrt(((a_1^2 + a_2^2 ) h)/(2g (a_1^2 - a _ 2^2))) `
D. ` (2 a _ 1 a _ 2 gh )/(sqrt(a_1^2- a _ 2 ^2 )) `

Answer

A

Explanation

Using Bernoulli’s concept ` P _ 1 + (1)/(2 ) rho v _ 1 ^ 2 + rho gh _1 = P_2 + (1)/(2) rho v_ 2 ^2 + rho gh_2 `
Hence, `Q = a _ 1 a _ 2 sqrt((2gh)/(a _ 1 ^2 - a _2 ^ 2 )) ` (Volumetric flow )