If there is a reduction in the size of a water pipe does the pressure increase decrease or stay the same? In this video we will be going over how to find the velocity and pressure in a water pipe that has a reduction in size. We are given the the pressure at point one of 1,000 kilo pascals, velocity at point 1 of 2 m/s, diameter at point 1 of 1 meter and diameter at point 2 of .25 meters.
We will be using the Bernoulli equation. The bernouilli equation is used to find out how much energy is in the pipe. There are 3 portions of the equation pressure energy, potential energy and kinetic energy.
Being that there is no average height difference between point 1 and point 2 we will elimate the potential energy portion of the equation.
The energy is conserved so both point 1 and point 2 in theory have the same energy. This means that we can take the pressure energy and kineticenergy portion of the bernouilli equation for both point 1 and point 2 and set them equal to one another.
Now in order to get the equation down to only one unsolved variable we must find the velocity. In order to do so we must know that the volume of water per second at point 1 must equal the volume per second at point 2. So if we reduce the size of the pipe the velocity must increase to accommodate the same volume of water. Setting the 2 points volumes equal to each other and rearranging the formula we get that the velocity at point 2 is 32 m/s
Now that we have the velocity at point 2 we can begin solving the bernoullis equation.
It is important to make sure you are in the correct units when completing these problems. For example 1,000 kilo pascals should be converted to pascals or newtons per meter squared, density should be in kilograms per meter cubed and velocity should be in meters per second.
After we plug in all of the numbers and rearrange the formula we get that the pressure at point 2 is 490 kilo pascals or 490,000 N/m squared
As a foot note to this problem when I was working this out I had some issues figuring out how the units of the kinetic energy portion ended up being in pascals. So I have placed a slid that goes over how the units are the same as a pascal.
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Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.
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