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

`P_t=5066250.0696\ Pa=50\ atm`

Step-by-step 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* 101325=202650\ Pa`

Now the force of flow of water:

`F=P* A`

now we find cross sectional area of the pipe:

`A=(\pi.d^2)/(4)`

`A=\pi *(0.1)/(4)`

`A=0.007854\ m^2`

Therefore,

`F=202650* 0.007854`

`F=1591.6094\ N`

Now the area at throat:

`A_t=(\pi.d_t^2)/(4)`

`A_t=(\pi* 0.02^2)/(4)`

`A_t=0.000314\ m^2`

Therefore pressure at throat:

`P_t=(F)/(A_t)`

`P_t=(1591.6094)/(0.000314)`

`P_t=5066250.0696\ Pa=50\ atm`