How Do Velocity and Pipe Diameter Affect Water Flow in Gravity-Fed Systems?

[birddog]

Hello there,

Im trying to figure this assignment question and I have hit hurdle. Can someone please help with figuring out what the velocity and pipe diameter will be??

Question:
In a plant 20m3(cubic)/h of water at 20 degrees C is to flow via gravity from a storage tank to another one. the difference in elevation is 15m and total pipe length is 50m.

I thought it would be 9.81 m/s because of gravity but that seems too fast.
Can someone please help.

Thanks in advance!

 

[CFDFEAGURU]

See your first thread.

https://www.physicsforums.com/showthread.php?t=338253

Thanks
Matt

 

[Mene]

Hello! I can provide some insight on the relationship between velocity and pipe diameter in this scenario. The velocity of water flowing through a pipe is dependent on several factors, including the diameter of the pipe, the pressure difference, and the fluid properties (such as density and viscosity). In this case, the velocity will be affected by the diameter of the pipe, as well as the pressure difference caused by the difference in elevation and the total pipe length.

To determine the velocity of the water, you can use the Bernoulli's equation, which states that the sum of the pressure, potential energy, and kinetic energy of a fluid in a pipe must remain constant. In this case, the potential energy (due to the elevation difference) will be converted into kinetic energy as the water flows through the pipe.

To calculate the velocity, you can use the following equation:

v = √(2gΔh)

where v is the velocity, g is the acceleration due to gravity (9.81 m/s²), and Δh is the difference in elevation (15m in this case). This will give you a velocity of 17.22 m/s, which is quite fast. This is because the pressure difference and pipe length also play a role in determining the velocity.

As for the pipe diameter, it is important to choose a diameter that can accommodate the desired flow rate without causing excessive pressure drop. This can be calculated using the Darcy-Weisbach equation, which takes into account the fluid properties, pipe length, and flow rate. Without knowing the specific details of the pipe and fluid properties, it is difficult to determine the exact diameter needed. However, you can use online calculators or consult with an engineer to determine the appropriate diameter for your specific scenario.

I hope this helps with your assignment question. Good luck!