# Fluid flow/pressure in a pipe going uphill

• j3dwards
In summary: PA + ρgyA + 0.5ρvA2 = PB + ρgyB + 0.5ρvB2So yA > yB and I think the velocities are the same? So does that make the pressure higher at B?correct on both counts.If the water were not flowing what would your answer be?Are you familiar with Pascals law?PB = PA + ρghAgain making pressure higher B than A!correct on both counts.But what about C? Is the pressure at C the same as the pressure at B?No, not the same, apply Bernoulli's equation again.
j3dwards

## Homework Statement

Water is flowing along a pipe. Points B and C in the pipe are at the same height but point A is at a higher elevation.The pipe has the same cross-sectional area at points A and B but is wider at point C. Rank in order from largest to smallest, the pressures at the three points A, B, C. Briefly explain your reasoning.

## Homework Equations

Bernoulli''s equation?

## The Attempt at a Solution

Largest to smallest in order: A, B, C

Pressure highest at A because A is uphill, then B because it has a smaller cross sectional area than C, and then C because greatest cross sectional area.

But I'm not sure if pressure is higher at C because it's pushing fluid uphill?

Are you familiar with Pascals law?

j3dwards said:

## Homework Statement

Water is flowing along a pipe. Points B and C in the pipe are at the same height but point A is at a higher elevation.The pipe has the same cross-sectional area at points A and B but is wider at point C. Rank in order from largest to smallest, the pressures at the three points A, B, C. Briefly explain your reasoning.

## Homework Equations

Bernoulli''s equation?

## The Attempt at a Solution

Largest to smallest in order: A, B, C

Pressure highest at A because A is uphill, then B because it has a smaller cross sectional area than C, and then C because greatest cross sectional area.

But I'm not sure if pressure is higher at C because it's pushing fluid uphill?

Is the pressure at A higher because it's uphill? What's the pressure at B relative to the pressure at A? Did you apply Bernoulli's equation to see if your reasoning is valid?

SteamKing said:
Is the pressure at A higher because it's uphill? What's the pressure at B relative to the pressure at A? Did you apply Bernoulli's equation to see if your reasoning is valid?

PA + ρgyA + 0.5ρvA2 = PB + ρgyB + 0.5ρvB2

So yA > yB and I think the velocities are the same? So does that make the pressure higher at B?

correct on both counts.

billy_joule said:
Are you familiar with Pascals law?

PB = PA + ρgh

Again making pressure higher B than A!

billy_joule said:
correct on both counts.
But what about C? Is the pressure at C the same as the pressure at B?

No, not the same, apply Bernoulli's equation again.

## 1. What causes fluid to flow uphill in a pipe?

Fluid flows uphill in a pipe due to the force of gravity. When a pipe goes uphill, the fluid inside is moving against the direction of gravity. However, the pressure exerted by the fluid at the bottom of the pipe is higher than at the top, causing the fluid to move upwards.

## 2. Does the diameter of the pipe affect fluid flow uphill?

Yes, the diameter of the pipe does affect fluid flow uphill. A larger diameter pipe will allow for a greater volume of fluid to flow uphill, while a smaller diameter pipe will have a slower flow rate due to higher frictional forces.

## 3. How does the slope of the pipe impact fluid flow uphill?

The slope of the pipe, also known as the incline or gradient, affects the speed of fluid flow uphill. A steeper slope will result in a faster flow rate, while a gentler slope will have a slower flow rate. This is because a steeper slope creates a greater pressure difference between the top and bottom of the pipe, allowing for a faster flow.

## 4. Can fluid flow uphill in a pipe without any external force?

No, fluid cannot flow uphill in a pipe without any external force. As mentioned before, the force of gravity is necessary for fluid to flow uphill. If there is no external force, such as a pump, to create a pressure difference, the fluid will remain stagnant.

## 5. How does the viscosity of the fluid affect flow uphill in a pipe?

The viscosity of the fluid, or its resistance to flow, can impact the flow rate uphill in a pipe. Higher viscosity fluids, such as honey, will have a slower flow rate compared to lower viscosity fluids, such as water. This is because the higher viscosity creates more frictional forces, slowing down the flow rate.

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