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Evgen
2 months ago
12

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 pressu

re 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
Physics
1 answer:
Ostrovityanka [3.2K]2 months ago
6 0

Response:

P_t=5066250.0696\ Pa=50\ atm

Clarification:

Provided:

  • diameter of the pipe, d=0.1\ m
  • the throat's diameter, d_t=0.02\ m
  • flow velocity, v=0.4\ m.s^{-1}

The pressure in the pipe is twice the atmospheric pressure:

P=2\times 101325=202650\ Pa

To find the water's flow force:

F=P\times A

we now calculate the cross-sectional area of the pipe:

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

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

A=0.007854\ m^2

Thus,

F=202650\times 0.007854

F=1591.6094\ N

Next, we determine the area at the throat:

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

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

A_t=0.000314\ m^2

So, the pressure at the throat becomes:

P_t=\frac{F}{A_t}

P_t=\frac{1591.6094}{0.000314}

P_t=5066250.0696\ Pa=50\ atm

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