How to determine the tank volume and power requirement?

[t0mm02]

Homework Statement

A conventional stirred tank is used for rapid mixing in a water treatment plant with a flow of 100 x 106 L/day. The water temperature is 10°C. Determine the tank volume and power requirement?

Relevant Equations

V = Q (flow rate) x θ (times the hydraulic detention time)

Hello everyone. I have to determine the tank volume and power requirement of a tank. The teacher has done it the following way, however, I don't understand the process.

 

[Gordianus]

The 69 m³ tank is filled and emptied every 60 seconds. This gives you 1.15 m³/s. Now, if you multiply 1.15 m³/s by 86400 s (one day) you get 99360 m³, very close to 100x10⁶ liters. As for the power, you haven't given any data.

 

[t0mm02]

The 69 m³ tank is filled and emptied every 60 seconds. This gives you 1.15 m³/s. Now, if you multiply 1.15 m³/s by 86400 s (one day) you get 99360 m³, very close to 100x10⁶ liters. As for the power, you haven't given any data.

How do you calculate the Volume though? I don't understand what he did on that picture to work it out.

 

[Gordianus]

What is the volume of a tank that, filled and emptied every 60 seconds, amounts to 100x10⁶ liters in a day?

 

[t0mm02]

What is the volume of a tank that, filled and emptied every 60 seconds, amounts to 100x10⁶ liters in a day?

I have no idea, that is what I am asking you

 

[Gordianus]

Let's say the tank has volume $V$ and that every $T= 60$ seconds it is filled and emptied. You repeat this cycle 1440 times (the number of minutes in one day) and the total exchanged volume is 100x10⁶ liters. Can you figure out the volume of the tank?

 

[Lnewqban]

How do you calculate the Volume though? I don't understand what he did on that picture to work it out.

Do you understand the concept of hydraulic detention time?
Imagine a river flowing into a lake and then continuing on downstream that lake.
The HDT in that case would be the time that it would take for that upstream river flow to completely fill that empty lake.

Copied from
https://baywork.org/wp-content/uploads/2016/05/Warm-Up-Ticket-Napa-Great-Shake.pdf

"Hydraulic detention time (HDT) also known as hydraulic retention time (HRT) is a measure of the average length of time that a compound (in this case wastewater) remains in a treatment tank or unit. Simply stated if you started to fill a tank with wastewater the detention time is the average amount of a time that a drop of that water will remain in the treatment tank before the tank fills and that drop of water flows out of it. This is important because as wastewater passes through a treatment tank it must stay in the tank for the necessary period of time in order to be adequately treated."

What your teacher did was converting liters to cubic meters and days to seconds, then calculating how much volume of water would flow into a container during 60 seconds at that given rate of flow.

Now, regarding power, they will need to tell you the pressure loss inside that tank, if they are referring to pump power.

Please, see:
https://www.engineeringtoolbox.com/pumps-power-d_505.html

As they give you the temperature of the water, you can estimate its density.