Question

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?

Answer #1

Bernoulli's law says that energy is conserved in the flow (no
viscous or turbulent losses):

P + 1/2 d v^2 + dgh = constant

where d is the density of the fluid, P is pressure, v is linear
velocity, and h is the height of the flow. If the pipe is
horizontal, h is the same at both points, so

P1 + 1/2 d v1^2 + dgh = P2 + 1/2 d v2^2 + dgh

P2 - P1 + 1/2 d (v2^2 - v1^2) = 0

The volume velocity u is linear velocity times cross-sectional
area. If the fluid is incompressible, then the volume velocity is
constant.

u = v1 (pi r1^2) = v2 (pi r2^2)

P2 - P1 + 1/2 d (v2^2 - v1^2) = 0

P2 - P1 + 1/2 d (u / (pi r2^2) )^2 - (u / (pi r1^2) )^2 =0

u^2 = - (P2 - P1) / { 1/2 d (1/r2^4 - 1/r1^4) / pi^2 }

= - (31.5e3 N/m^2 - 23.4e3 N/m^2) / { 1/2 (1e3 kg/m^3) (1/(0.067/2
m)^4 - 1/(0.053/2 m)^4) / pi^2 }

=12.9e-5 m^4/s^2

u = 11.364e-3 m^3/s^2

x (1000 L / 1 m^3) = 11.364 L/s

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 7.8 cm diameter horizontal pipe gradually narrows to 6.8 cm .
When water flows through this pipe at a certain rate, the gauge
pressure in these two sections is 33.0 kPa and 22.6 kPa ,
respectively.
What is the volume rate of flow?

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 7.2 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 6.8 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?

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