Flow through a pipe, pressure, velocity, Bernoulli, etc

In summary, the conversation discusses the effects of changing the pump volumetric output and pipe diameter on the pressures and heights within a pipe system. It is determined that an increase in pump output or a decrease in pipe diameter will result in an increase in flow velocity, leading to a decrease in pressure and height at all locations (except D). However, the answer suggests that the pressures and heights will actually increase at all locations, as there is a constant pressure drop along the pipe and an increase in flow velocity may also increase flow resistance. This may cause a discrepancy in the expected results.
  • #1
Gyro
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Hello everyone,
Thank you to all who offer their help.

Homework Statement



If the volumetric output of the pump were increased, keeping the pipe diameter constant, would the pressures at A, B, and C increase or decrease? Would the heights within each column at each location rise or fall? Explain.

If smaller pipe were used, keeping pump volumetric output the same, would the pressures at A, B, and C increase or decrease? How would the heights of each column change? Explain.

Homework Equations



Flow rate = Area x Velocity [1]

Bernoulli's energy balance: KE1 + PE1 + GPE1 = KE2 + PE2 + GPE2 [2]
where
KE = kinetic energy, PE = potential energy (from pressurized fluid), GPE = gravitational potential energy (from height difference from reference point)

The Attempt at a Solution



My answer follows:

In the first situation, when pump volumetric output is increased:
From [1]: if Flow rate increases, and Area is const., then Velocity increases.
From [2]: if Velocity increases, KE increases, so KE2 - KE1 = some value
since there is no height change along the pipe, GPE2 - GPE1 = 0
so to balance energies, a decrease in PE must occur, which means a decrease in the pressure.
Therefore, an increase in pump volumetric flow will decrease the pressures at A, B, and C and thus make the heights of each column fall accordingly.

In the second situation, when volumetric output is const., and diameter of pipe is reduced:
From [1]: if Area is decreased, and Flow rate const., then Velocity increases, as in the first situation. Again, KE increases, GPE const., PE has to decrease, and pressures decrease. Again, the heights of liquid fall for each column. Situation 1 and 2 both increase fluid velocity, which drops pressure, according to Bernoulli, and the heights will fall.Problem is, the answer says the pressures and heights increase at all locations (except D as it is at atmospheric pressure) for both scenarios.

What am I not understanding? Any help is appreciated.
 

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  • #2
There is a pressure drop along the pipe, and given the diameter and flow rate are constant the dp/dx should be constant. What happens with flow resistance as flow velocity increases?

What is the flow resistance of a smaller pipe for the same volumetric flow rate?
 

What is flow through a pipe?

Flow through a pipe refers to the movement of a fluid, such as water or gas, through a cylindrical pipe. This flow can be either laminar (smooth and orderly) or turbulent (chaotic and irregular).

How does pressure affect flow through a pipe?

Pressure is one of the main driving forces behind flow through a pipe. When there is a difference in pressure between the two ends of a pipe, the fluid will flow from the higher pressure region to the lower pressure region. This is known as the pressure gradient.

What is the relationship between velocity and pressure in flow through a pipe?

According to Bernoulli's principle, as the velocity of a fluid increases, the pressure decreases. This means that in a pipe with a constant diameter, as the fluid moves faster, the pressure decreases. This is why water can shoot out of a hose with greater force when you block part of the opening.

What is the Bernoulli equation and how is it used in flow through a pipe?

The Bernoulli equation is a fundamental principle in fluid dynamics that relates the pressure, velocity, and elevation of a fluid at any point in a pipe. It can be used to calculate the change in pressure or velocity at different points in a pipe, and is essential for understanding and predicting flow patterns.

How does the shape and size of a pipe affect flow through it?

The shape and size of a pipe can have a significant impact on the flow of a fluid through it. A larger diameter pipe will allow for greater flow rate and less resistance, while a smaller diameter pipe will cause the fluid to flow faster and experience more resistance. The shape of the pipe can also affect the flow pattern, with curved pipes creating more turbulence than straight pipes.

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