Question

Fuel oil density `820" kg/m"^3` flows through a venturi meter having a throat diameter of 4.0 cm and an entrance diameter of 8.0 cm. The pressure drop between the entrance and the throat is 16 cm of Mercury. The density of mercury is `13600" kg/m"^3`?

Answer 1

The flow rate is `=0.0094m^3s^-1`

Explanation:

Apply Bernouilli's Equation between points `A` and `B`

`p_A+1/2rho v_A^2+rhogh_A=p_B+1/2rho v_B^2+rhogh_B`

The flow rate is constant in the pipe

`Q=v_AxxA=v_Bxx B`

where

`A=pid_A^2/4=pixx0.08^2/4`

and

`B=pid_B^2/4=pixx0.04^2/4`

`v_Axxpixx0.08^2/4=v_Bxxpixx0.04^2/4`

`v_A=v_B*(0.04/0.08)^2=0.25v_B`

`v_B=1/0.25v_A=4v_A`

But

`h_A=h_B`

Therefore,

`p_A+1/2rho v_A^2=p_B+1/2rho v_B^2`

The pressure difference is `Deltap=rhogh=13600*9.8*0.16=21324.8Pa`

`Deltap=21324.8=1/2rho(v_B^2-v_A^2)`

`1/2*820*(16v_A^2-v_A^2)=21324.8`

`v_A=sqrt(52.01/15)=1.86ms^-1`

The flow rate is

`q=1.86*pi*0.08^2/4=0.0094m^3s^-1`