Question

A venturi is constructed of a 10.0 cm pipe with a 2.0 cm diameter throat. Water pressure in the pipe is twice atmospheric pressure and it flows with a velocity of 0.40 m/s. What is the pressure in the throat?

a) 2.0 atm
b) 0.49 atm
c) 2.5 atm
d) 1.5 atm

Answer 1

Answer:

$P_t=5066250.0696\ Pa=50\ atm$

Explanation:

Given:

• diameter of pipe, $d=0.1\ m$

• diameter of throat, $d_t=0.02\ m$

• velocity of flow, $v=0.4\ m.s^{-1}$

Pressure in the pipe is twice the atmospheric pressure:

$P=2\times 101325=202650\ Pa$

Now the force of flow of water:

$F=P\times A$

now we find cross sectional area of the pipe:

$A=\frac{\pi.d^2}{4}$

$A=\pi \times\frac{0.1}{4}$

$A=0.007854\ m^2$

Therefore,

$F=202650\times 0.007854$

$F=1591.6094\ N$

Now the area at throat:

$A_t=\frac{\pi.d_t^2}{4}$

$A_t=\frac{\pi\times 0.02^2}{4}$

$A_t=0.000314\ m^2$

Therefore pressure at throat:

$P_t=\frac{F}{A_t}$

$P_t=\frac{1591.6094}{0.000314}$

$P_t=5066250.0696\ Pa=50\ atm$