Question

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.

Answer #1

Here,

radius of the 7 cm pipe, r1 = 7/2 = 3.5 cm

radius of pipe, r2 = 5/2 = 2.5 cm

let the speed of the flow is v1 and v2

Using equation of continuity

pi * 3.5^2 * v1 = pi * 2.5^2 * v2

Using Bernoulli's equation

P1 + 0.50 * p * v1^2 = P2 + 0.50 * p * v2^2

32000 + 0.50 * 1000 * v1^2 = 25000 + 0.50 * 1000 * v2^2

solving for v1 and v2

v1 = 2.22 m/s

v2 = 4.35 m/s

volume flow rate = pi * r1^2 * v1

volume flow rate = pi * 0.035^2 * 2.22

**volume flow rate = 0.0085 m^3/s**

**the volume flow rate is 0.0085
m ^{3}/s**

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 33.0 kPa and 23.0 kPa ,
respectively.
What is the volume rate of flow?

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.

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 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 6.7 cm diameter horizontal pipe gradually narrows to 5.3 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 31.5 kPa and 23.4 kPa ,
respectively.What is the volume rate of flow?

A 6.8 cm diameter 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 33.0 kPa and 24.0 kPa, respectively. What is
the volume rate of flow?

A 6.6 cm diameter 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 30.0 kPa and 24.0 kPa, respectively. What is
the volume rate of flow?

Water flows through a horizontal pipe at a rate of 2.3 m3/s. A
pressure gauge placed on a 40 cm diameter section of the pipe reads
210.3 kPa. What is the gauge pressure in a section of pipe where
the diameter is constricted to 35 cm and what has caused this
change in pressure?

In a section of horizontal pipe with a diameter of 4.0 cm, the
pressure is 115 kPa and water is flowing with a speed of 1.5 m/s.
The pipe narrows to a 3.0-cm diameter. What is the pressure in kPa
in the narrower region? Treat the water as an ideal incompressible
fluid.

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