Question

Describe the construction and working of venturimeter and obtain an equation for the volume of liquid flowing per second through a wider entry of the tube.

Answer 1

Venturimeter : This device is used to measure the rate of flow (or say flow speed) of the incompressible fluid flowing through a pipe. It works on the principle of Bernoulli’s theorem. It consists of two wider tubes A and A’ (with cross sectional area A) connected by a narrow tube B (with cross sectional area a). A manometer in the form of U-tube is also attached between the wide and narrow tubes. The manometer contains a liquid of density ‘ρ_m ’. 

Let P₁ be the pressure of the fluid at the wider region of the tube A. Let us assume that the fluid of density ‘ρ’ flows from the pipe with speed ‘v₁ ’ and into the narrow region, its speed increases to ‘v₂ ’. According to the Bernoulli’s equation, this increase in speed is accompanied by a decrease in the fluid pressure P₂ at the narrow region of the tube B. Therefore, the pressure difference between the tubes A and B‘ is noted by measuring the height difference (∆P = P₁ – P₂ ) between the surfaces of the manometer liquid. 

From the equation of continuity, we can say that Av₁ = av₂ which means that

From the above equation, the pressure difference

The volume of the liquid flowing out per second is