Question

A 7.2 cm diameter horizontal pipe gradually narrows to 4.8 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.0 kPa and 26.0 kPa , respectively.

What is the volume rate of flow?

Express your answer to two significant figures and include the appropriate units.

Answer #1

Given,

d1 = 6.3 cm ; d2 = 3.4 cm ; P1 = 32 k Pa and P2 = 22.6 kPa

We need to find the volume rate flow.

We know that,

A1v1 = A2v2

v2 = (A1/A1) v1 = (d1/d2)^{2} v1

We know from Bernaulli's equation that,

P1 + 1/2 rho v1^{2} + h1 rho g = P2 + 1/2
rho v2^{2} + h2 rho g

substituting the value of v2 we get

P1 + 1/2 rho v1^{2} + 0 = P2
+ 1/2 rho [(d1/d2)^{2} x
v1] ^{2} + 0 = P2
+ 1/2 rho (d1/d2)^{4}
v1^{2} +

solving for v1^{2} we get

v1^{2} = 2 (P1 - P2) / [ rho
(d1/d2)^{4} - 1 ]

putting in the values:

v1^{2} = 2 ( 33 - 26 ) x 10^{3} / [ 1000 x (7.2
x 10^{-2} / 4.8 x 10^{-2})^{4} - 1 ]

v1 = 1.66 m/s

So the volume rate flow will be:

A1v1 = pi (d1/2)^{2} x v1 = 3.14 x 7.2 x 7.2 x
10^{-4} x 1.66 / 4 = 6.76 x 10^{-3} m^{3}/s
(aprox)

**Hence, Volume flow rate = 6.76 x 10 ^{-3}
m^{3}/s (aprox)**

A 6.4 cm diameter horizontal pipe gradually narrows to 3.9 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 30.5 kPa and 25.2 kPa ,
respectively.
What is the volume rate of flow?
Express your answer to two significant figures and include the
appropriate units.

A 7.0-cm-diameter horizontal pipe gradually narrows to 4.0 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 32.0 kPa and 24.0 kPa ,
respectively.
What is the volume rate of flow? Express your answer using two
significant figures.

A 7.0-cm-diameter horizontal pipe gradually narrows to 5.0 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 32.0 kPa and 25.0 kPa ,
respectively.
What is the volume rate of flow?
Express your answer using two significant figures.

A 7.0-cm-diameter horizontal pipe gradually narrows to 5.0 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 33.0 kPa and 23.0 kPa ,
respectively.
What is the volume rate of flow?

A 6.3 cm diameter horizontal pipe gradually narrows to 4.5 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 31.0 kPa and 26.0 kPa ,
respectively. What is the volume rate of flow?

A 6.8 cm diameter pipe gradually narrows to 4.0 cm. When water
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When water flows through this pipe at a certain rate, the gauge
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Water flows through a horizontal pipe at a rate of 2.3 m3/s. A
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Liquid flows through the first segment at a speed of 4 m/s.
a- what are the speeds in the second and third segments?
b- what is the volume flow rate through the pipe?

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