Water is flowing through a tube 1 cm in diameter at a rate of 0.000942 m3/min a)

ID: 1462993 • Letter: W

Question

Water is flowing through a tube 1 cm in diameter at a rate of 0.000942 m3/min

a) What is the velocity of the water in the tube?

b) If the tube narrows to a nozzle with a diameter of 1 mm, what is the velocity of the water in the nozzle?

c) What is the rate of water flow through the nozzle in m3/min?

d) If, while the water is flowing, the pressure on the walls of the 1 cm tube is 200 kPa, what is the pressure on the walls of the 1mm nozzle?

e) If a valve at the outlet end of the nozzle is shut what will the pressure and flow rate be?

_________________________ and ______________________________

Radius, r = D /2 = 1 cm /2 = 0.5 cm = 0.005 m

Expression for flow rate:

Q = (A)(v)

Q = (r)²)(v)

9.42 x 10-4 = (0.005)²)(v)

v =11.99 m/s

= 12 m/s ( round off to 2 signiicant digits )

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(b)

If diameter is 1 mm, the radius, r = D / 2 = 0.5 mm = 0.0005 m

Q = (r)²)(v)

9.42 x 10-4 = (0.0005)²)(v)

v = 1199 m/s

= 1200 m/s ( round off to 2 signiicant digits )

Its speed increases by 100 times as compared to speed in part (a )

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( c)

Flow rate through nozzle:

Q = Av

= (r)²)(v)

= (0.0005)²)(1200 m/s)

= 9.42 x 10-4 m3 /s

= 1.57 x 10-5 m3 /min

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