**Gauge Pressure**

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## Question “Gauge Pressure”

The 3.0 cm-diameter water line in the figure splits into two 1.0 cm-diameter pipes. All pipes are circular and at thesame elevation. At point A, the water speed is 2.0 m/s and the gauge pressure is 50 kPa.What is the gauge pressure at point B?

## Answer

**Prepare:**

the gauge pressure at point 1.

the gauge pressure at point A.

All pipes are therefore circular and are located at the same height.

Bernoulli can express the equation that relates pressure *to p* speed and height *_ y* at all points along a streamline of an ideal fluid as follows:

These two points are at the same elevation so

The above equation is therefore now

The gauge pressure at point A can therefore be expressed as

. . . . . . (1)

Here,

Speed of fluid at point A

Speed at point B HTML3_

Density for the fluid

**Figure:**

As shown below, the water pipe is split into two smaller pipes.

**Solve:**

**Given data**

The diameter of the large pipe,

The diameter of each small tube,

The speed at which the water flows at point A,

The gauge pressure at point B,

You can express the volume flow rate for water through point A as

The cross-sectional area for the pipe is shown here

The above equation is therefore now

. . . . . . (2)

The volume flow rate for water through each small pipe can also be expressed in this way

. . . . . . (3)

The given figure shows that the volume flow of water at point A equals the sum between the volume rate through one small tube and the volume rate through the other.

In the above relation, substitute the equations **(2)** and **(3)**.

. . . . . . (4)

**(4)** is the equation that determines the speed at which water moves from point A to point B.

The equation **(1)** can be used to calculate the gauge pressure at point A.

## Conclusion

Above is the solution for “**Gauge Pressure**“. We hope that you find a good answer and gain the knowledge about this topic of **science**.