Question

In the figure, water flows through a horizontal pipe and then out into the atmosphere at a speed v₁ = 16.0 m/s. The diameters of the left and right sections of the pipe are 5.20 cm and 3.00 cm. (a) What volume of water flows into the atmosphere during a 10 min period? In the left section of the pipe, what are (b) the speed v₂ and (c) the gauge pressure?

Question 1 In the figure, water flows through a horizontal pipe and then out into the atmosphere at a speed vi - 16.0 m/s. The diameters of the left and right sections of the pipe are 5.20 cm and 3.00 cm. (a) What volume of water flows into the atmosphere during a 10 min period? In the left section of the pipe, what are (b) the speed v2 and (c) the gauge pressure? V2 dc (a) Number (b) Number (c) Number Units Units Units

Answer 1

The relationship between flow rate (Q )and velocity is

  

O-Au.

Where, A is area of cross section of the pipe

Area of the left cross section :

  

5.20 x 10-2 ) = 21.24 x 10-4 m?

Area of right cross section of pipe :

  

A1 = π x (う 2 10-2 ) = 7.07 x 10-4 m 7.07 x 104m

From the continuity equation

Q2 = Q1

or,   

Given,

So,

For the right end of pipe

  

For left end of pipe ,

  

(a) The volume of water flows into the atmosphere during a 10 min period will be

(b) The speed $v_{2}$ , as calculated above, is 5.3 m/s .

(c) Gauge pressure is given by

Where, is density of fluid, for water it is 1000 kg/m³ .

To find the pressure in the left section, use Bernoulli’s equation:

Here,

So,

or,   

Here,

So,

Hence, gauge pressure at the left end of pipe will be

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