Calculating Fill Time for a Cylindrical Grow-Out Tank | Water Flow Question

[majin]

I am stuck on questions like this can anyone help
How long would it take to fill a cylindrical grow-out tank (2m high, 8m diameter, 10% freeboard) from an inlet pump delivering 25 litres of water every minute through a 25mm pipe that has 4 spray outlets?

first of all I know that the 4 spray outlets are irrelevant to the quetion and are a decoy. as well as this i know that the pipe is cylindrical

tank volume with freeBoard =90.47786842
25 L/min converts into 0.025 m3/min
to get that into m3 per sec(delivery rate) I times it by 60=1.5m3/sec

So to get the answer do I divide the delivery rate(1.5) into the tank volume i.e(90/1.5) OR do I use the delivery rate as a height(h) variable and work out volume of pipe i.e(pi*h*r*r)and then divide the volume of the pipe into the tank volume i.e(vt/vp) to get the amount in secs? any help will be greatly appreciated

 

[verty]

That's one odd pump, delivering 0.025 m3/min but 1.5m3/sec.

You can't use the delivery rate as a height variable because height is measured in metres and delivery rate is m3/s or similar. It's always good to look at the units: volume is m3, delivery rate is m3/s.

 

[tacman]

To calculate the fill time for the cylindrical grow-out tank, we will need to use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to calculate the volume of the tank with freeboard. Using the given dimensions, we can plug them into the formula: V = π(4m)²(2m) = 100.53m³.

Next, we need to convert the water flow rate from liters per minute to cubic meters per second. We can do this by multiplying the flow rate (25 liters per minute) by the conversion factor of 0.001. This gives us a flow rate of 0.025m³/s.

Now we can use the formula t = V/Q, where t is the time, V is the volume, and Q is the flow rate. Plugging in the values, we get t = 100.53m³/0.025m³/s = 4021.2 seconds.

However, we need to account for the freeboard in the tank. Since the tank has a 10% freeboard, we need to add an additional 10% to the volume. This gives us a final volume of 110.58m³.

Using the same formula, t = V/Q, we get t = 110.58m³/0.025m³/s = 4423.2 seconds.

Therefore, it would take approximately 4423 seconds (or 73.7 minutes) to fill the cylindrical grow-out tank with the given dimensions and water flow rate.