Question

A converging-diverging tube, called a venturi, develops a low-pressure airflow in the throat capable of sucking a heavier fluid up a reservoir, as shown in the figure. This is the working principle of paint spraying guns. The specific masses of air and liquid are respectively , while the throat and discharge diameters in the atmosphere are respectively D1 and D2.
If the elevation height above the liquid level in the reservoir is h and the gravitational acceleration is g, deduce an expression for the volumetric flow rate of air Q sufficient to begin to bring fluid from the reservoir into the throat. Despise the losses.

Mass conservation:

pe p D2 DL Pa ar h Pa g p líquido 1 Bernoul ppV2pgz cte ap (V.n) dA ou 0 0= dv dt A

Answer 1

Let the volume flow rate of air be Q

Now the velocity of air flow will be:

4Q A TD

Now at the throat, using the continuity equation the velocity will be

4인 UT AT

Now applying Bernoulli's theorem

p+ Pa -pgh Pa

122gh 2

1 4Q 1 gh DD

Hence

πρ gh(D1D) Q = 4ρ (D3

Hope it helps. Cheers!!