Calculating Flow Rate and Fill Time for Gravity-Fed Water Trucks

[beachfarmer]

Homework Statement

Greetings:

I'm a bit rusty on Bernouli's Equation...any help is appreciated.

I would like to fill two 5,000 gallon water trucks from a 20,000 gallon circular water storage tank by gravity. Here is the info:

1. The 20,000 gallon storage tank is a cylinder and sits vertical. It is approximately 15 feet in diameter and 15 feet tall. The exit orfice is at the center on the bottom of the tank.

2. There is 100 feet of 12 inch PVC piping from the tank to a tee that reduces each branch to 6 inches. There is an additional 10 feet of 6 inch piping off each branch which are terminated with a spigot. At each spigot the truck hose is connected, and when opened, fills the water tanker trucks.

3. Assume two 90 degree elbows in the12 inch PVC and another 90 degree elbow in each 6 inch branch.

4. Assume 5 feet of head between the storage tank orfice and the spigot and that the orfice elevation is equal to the top of the water truck tank.

Questions:

1. What is the flow rate at the spigot?
2. How long does it take to fill the 2 trucks simultaneously?

Homework Equations

Bernoulli and pipe flow

The Attempt at a Solution

Need your help!..any info is appreciated

 

[CWatters]

I've no idea how to approach your problem but this software looks like it can do it and here is a free trial version..

http://www.pipeflow.com/

I've no connection with the company that produced it.

 

[rude man]

Homework Statement

Greetings:

I'm a bit rusty on Bernouli's Equation...any help is appreciated.

I would like to fill two 5,000 gallon water trucks from a 20,000 gallon circular water storage tank by gravity. Here is the info:

1. The 20,000 gallon storage tank is a cylinder and sits vertical. It is approximately 15 feet in diameter and 15 feet tall. The exit orfice is at the center on the bottom of the tank.

2. There is 100 feet of 12 inch PVC piping from the tank to a tee that reduces each branch to 6 inches. There is an additional 10 feet of 6 inch piping off each branch which are terminated with a spigot. At each spigot the truck hose is connected, and when opened, fills the water tanker trucks.

3. Assume two 90 degree elbows in the12 inch PVC and another 90 degree elbow in each 6 inch branch.

4. Assume 5 feet of head between the storage tank orfice and the spigot and that the orfice elevation is equal to the top of the water truck tank.

Questions:

1. What is the flow rate at the spigot?
2. How long does it take to fill the 2 trucks simultaneously?

Homework Equations

Bernoulli and pipe flow

The Attempt at a Solution

Need your help!..any info is appreciated

Before I look at this I would want the dimensions of the water truck tanks. It might make a difference whether those tanks are narrow and deep or wide and shallow. If you weren't given those dimensions in a problem set then maybe it doesn't, but I would like to know.

 

[CWatters]

Before I look at this I would want the dimensions of the water truck tanks. It might make a difference whether those tanks are narrow and deep or wide and shallow. If you weren't given those dimensions in a problem set then maybe it doesn't, but I would like to know.

I'm curious why that would make a difference?

The size of the pond at the bottom of a waterfall has no effect on the flow rate of the waterfall.

 

[rude man]

Like I said, I'm not sure.

Per your description, if I got it right, the spigot is 5' below the top of the truck tanks. At first the truck tanks are empty and the pressure p at the spigot is 1 at. But once the water level inside the truck tanks reaches the spigot level, p increases beyond 1 at. to ρgh where h is the height of the water column above the spigot. Which of course is building up continuously. For h > 0 the ensuing pressure buildup at the spigot will slow down the rate of storage tank outflow to accommodate Bernoulli, viz. p + ρgh + ρv²/2 is conserved, and p will be building up inside the truck tanks once the spigot level is reached.

Make any sense?

Minor edit.

 

[CWatters]

Like I said, I'm not sure.

Per your description, if I got it right, the spigot is 5' below the top of the truck tanks.

Ah ok I understand. I didn't spot that bit.

 

[NascentOxygen]

It seems as much an exercise in comprehension (i.e., mind reading) as physics. My interpretation:

The (sic) truck hose sounds singular, so most likely is the discharge hose from the base of the tanker, so it follows when filling via this route there is always water pressure to overcome.

You are filling (sic) the tankers, so the water in the tank being filled rises to the same level as the storage tank orifice. Might it be necessary to assume the truck tanks are 5m in height? Or maybe it doesn't matter?