Efficient Water Irrigation System Design for Optimal Flow: Homework Help

[Confuzzled]

Homework Statement

A water tank of 500litres is to deliver 1liter of water per hour to 3 locations each 15meters from the tank.


2. Homework Equations , i think...

Reynolds number?
Pressure? = pAhg/A of base
Flow rate = volume/time
Average velocity = flow rate / cross sectional area
Density = mass /volume
And another I am sure which I am unsure of?

The Attempt at a Solution

Volume = mass/ density
0.003m3 = 3kg (1 litre of water to 3 locations) / 1000kg/m3

Flow rate = volume / time
833x10-9 m3/s = 0.003/ 3600 (seconds in an hour)

My only problem with this is that I am unsure of how to work out the speed of flow & diameter of the pipework.
But also how do I ensure that there is enough pressure to keep the flowing going for 15meters?


Any support or guidance would be much appreciated, I've been racking my mind for hours.

Regards,
Confuzzled

 

[KataKoniK]

Scientist

Dear Confuzzled Scientist,

Thank you for your post. It seems like you have made a good start on solving this problem. To determine the flow rate and velocity of the water, you can use the equation you provided: flow rate = volume / time. This will give you the flow rate in m3/s, which you have calculated correctly to be 833x10-9 m3/s.

To determine the diameter of the pipework, you can use the equation for average velocity: average velocity = flow rate / cross sectional area. You already have the flow rate, so you just need to calculate the cross sectional area of the pipework. This can be done using the formula for the area of a circle: A = πr2, where r is the radius of the pipework. You can then rearrange this equation to solve for the radius, and then double the radius to get the diameter.

As for ensuring enough pressure to keep the flow going for 15 meters, you can use the equation for pressure: P = pAhg/A of base. In this case, p is the density of water (which you have correctly identified as 1000kg/m3), A is the cross sectional area of the pipework, h is the height of the water tank (which is given as 15 meters), and A of base is the area of the base of the tank. This will give you the pressure in Pascals (Pa). If you want to convert this to a more common unit like kilopascals (kPa), you can divide by 1000.

I hope this helps you solve the problem. Good luck with your calculations!