Help with a pipe, water, continuity and Bernoullie

• TFM
In summary, the problem involves finding the gauge pressure at a second point in a pipeline, given the speed and gauge pressure at a first point and the diameter change of the pipe. Using Bernoullies equation and the continuity equation, the speed at the second point is calculated to be 3/4 m/s. However, the incorrect placement of the height values in Bernoullies equation leads to a negative pressure, which is resolved by correcting the value for y2. The final answer is 162018.75.
TFM
[SOLVED] Help with a pipe, water, continuity and Bernoullie

Homework Statement

At one point in a pipeline the water's speed is: 3.0 m/s,
the gauge pressure is: 5.0*10^4.

Find the gauge pressure at a second point in the line, 11m lower than the first, if the pipe diameter at the second point is twice that at the first.

Homework Equations

Bernoullies Equation: P1 + density*g*y1 + 0.5*density*v1^2 = P2 + density*g*y2 + 0.5*density*v2^2

Continuity Equation: A1V1 = A2V2

The Attempt at a Solution

I work out the speed of v2 using continuity, with area-1 being pi*r^2, Area-2 being pi*4r^2,
This makes the speed 3/4 m/s

I themn put all known variables into Bernoullies equation, which gives me a negative pressure! (-53581.25) this cannot be right?

Any Ideas/Suggestions

TFM

TFM said:
I work out the speed of v2 using continuity, with area-1 being pi*r^2, Area-2 being pi*4r^2,
This makes the speed 3/4 m/s
Looks good.

I themn put all known variables into Bernoullies equation, which gives me a negative pressure! (-53581.25) this cannot be right?
No, it can't. What did you put for y1 & y2?

I first put y1 as 0, y2 as 11, then tried y1 as 1, y2 as 12

It should be y2 = -11, shouldn't it? -goves an answer of 162018.75

TFM said:
It should be y2 = -11, shouldn't it?
Yep.

Thanks

TFM

1. What is the principle of continuity?

The principle of continuity is a fundamental law in fluid mechanics that states that the mass of a fluid remains constant within a closed system. This means that the volume of fluid entering a pipe must be equal to the volume of fluid exiting the pipe, assuming there are no leaks or changes in density.

2. How does Bernoulli's equation apply to fluid flow in a pipe?

Bernoulli's equation states that the sum of kinetic energy, potential energy, and pressure energy in a fluid system remains constant. In a pipe, this means that as the fluid velocity increases, the pressure decreases. This principle is often used to explain the phenomenon of lift in airplane wings.

3. How can I calculate the flow rate of water in a pipe?

The flow rate of water in a pipe can be calculated using the continuity equation, which states that the volume flow rate (Q) is equal to the product of cross-sectional area (A) and velocity (v). In mathematical terms, this can be written as Q = A * v. The units for flow rate are typically measured in liters per second or cubic meters per hour.

4. How does the diameter of a pipe affect the flow of water?

The diameter of a pipe has a significant impact on the flow of water. According to the continuity equation, as the diameter of a pipe decreases, the velocity of the fluid must increase to maintain the same flow rate. This is why water can shoot out of a garden hose with much greater force when the nozzle is narrowed.

5. How can I ensure there is continuity in a pipe system?

To ensure continuity in a pipe system, it is important to minimize any sources of leakage and maintain a consistent cross-sectional area throughout the system. This can be achieved by regularly inspecting and repairing any cracks or holes in the pipes and ensuring that all fittings and connections are secure. Additionally, proper design and installation of pipe systems can help to maintain continuity and prevent disruptions in fluid flow.

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