# Filling a Tank with Water: Solving for Time

• Chase11
In summary, the problem asks how long it will take to fill a tank with 180 m^3 of water coming from a pipe with a velocity of 22 m/s and a diameter of 48 cm. Using the formula for volumetric flow rate, the time can be calculated to be 0.468 seconds.
Chase11

## Homework Statement

The water from a pipe flows into a tank of volume 180 m^3. If the tank is initially empty, how long will it take to fill the tank?

I know that water is coming out of the pipe with a velocity of 22 m/s, and the diameter of this end of the pipe is 48 cm.

## Homework Equations

This is what I don't know.
Is it v1A1=v2A2? or p1+1/2ρv1^2+ρgy1=p2+1/2ρv2^2+ρgy2?

## The Attempt at a Solution

v1A1=v2A2

22 m/s*.10898 (A1)=0?

You're kind of using the formula wrong. I might suggest calculating it with all the units explicitly stated and then look at the question again.

If you know the cross sectional area of the pipe and the average velocity of the water coming out of the pipe, to you know the formula for calculating the volumetric throughput rate coming out of the pipe?

Or - don't worry about the equation: just look at the geometry.
What is the volume of water flowing through the pipe each second?

You know how to find the volume of a cylinder right?

paisiello2 said:
You're kind of using the formula wrong. I might suggest calculating it with all the units explicitly stated and then look at the question again.

Okay so my units on each side will be meters^3/sec. I don't understand how to just get m^3 without taking out the velocity (which I am going to need to use right?)

Chestermiller said:
If you know the cross sectional area of the pipe and the average velocity of the water coming out of the pipe, to you know the formula for calculating the volumetric throughput rate coming out of the pipe?

The only formula I can find that I feel applies is V1A1=V2A2.
Is this not the correct equation to use?
Even if it is, my confusion is what goes on the right side of the equation? Being that V2 and A2 don't really apply to the information I am given.

Simon Bridge said:
Or - don't worry about the equation: just look at the geometry.
What is the volume of water flowing through the pipe each second?

You know how to find the volume of a cylinder right?

V=∏r^2h
∏(.325m)^2(.65m)=.2157m^3
How does this tell me the flow rate per second?

I'm sure your text or course notes talked about the formula for volumetric flow (you actually already stated it in context)?

Suppose you were standing next to the 48cm dia. pipe and you measured an h=1m length of pipe. You could wait for t=1 second and measure the volume of water V flowing by in that time and this would give you Q=V/t (the volumetric flow rate).

But V = Ah (volume)
and v = h/t (speed)
therefore Q = vA

Hopefully you can take it from there.

1 person
Since you are told that the flow rate is constant, the volume of water through the pipe in one second is the flow rate.

Don't worry about these terms right now. I am trying to get you off your dependence on memorizing equations.

V=∏r^2h
... that's the volume of a cylinder radius r and length h - good.
(It's better if you use "π" instead of "∏" there, but I can see what you mean.)

∏(.325m)^2(.65m)=.2157m^3
You used r=0.325m and h=0.65m ... why? Where do these figures come from?

How does this tell me the flow rate per second?
If the numbers you use have no relation to the problem then it won't of course.

The pipe is cylindrical with diameter d=0.48m
The water flows in the pipe at speed v=22m/s

The water leaving the pipe is basically a cylinder that grows in length... or it would be if it didn't fall etc. So imagine water pouring out the pipe in a long straight cylinder of water. You can work out the volume of the water leaving the pipe by working out the volume of the "cylinder" of water.

I'm asking you to use these figures, and the equation for the volume of a cylinder, to work out the volume of water that left the pipe in 1 sec.

If you know the volume of water that flows out the pipe in 1 second, then you can work out howm many seconds are needed to fill the tank.

1 person
Chase11 said:

## Homework Statement

The water from a pipe flows into a tank of volume 180 m^3. If the tank is initially empty, how long will it take to fill the tank?

I know that water is coming out of the pipe with a velocity of 22 m/s, and the diameter of this end of the pipe is 48 cm.

## Homework Equations

This is what I don't know.
Is it v1A1=v2A2? or p1+1/2ρv1^2+ρgy1=p2+1/2ρv2^2+ρgy2?

## The Attempt at a Solution

v1A1=v2A2

22 m/s*.10898 (A1)=0?
solution:
rate of flow can be determined by,
wkt v=22m/s area of hole:3.14*(0.24)*(0.24)
rate of flow =22*3.14*(0.24)*(0.24)m^3/s
time taken : 180m^3/(22*3.14*(0.24)*(0.24))m^3/s

## 1. How do you calculate the time it takes to fill a tank with water?

In order to calculate the time it takes to fill a tank with water, you will need to know the volume of the tank, the rate at which water is being added, and the initial amount of water in the tank. You can then use the formula time = volume / rate to find the time it takes to fill the tank.

## 2. What units should be used when solving for time to fill a tank with water?

The units used for solving for time to fill a tank with water will depend on the units used for volume and rate. For example, if the volume is given in liters and the rate is given in liters per minute, the time will be in minutes.

## 3. Can the time it takes to fill a tank with water be calculated if the tank is not being filled at a constant rate?

Yes, the time can still be calculated if the tank is not being filled at a constant rate. However, in this case, the rate at which water is being added will need to be expressed as an average rate over a certain period of time.

## 4. How does the height of the tank affect the time it takes to fill with water?

The height of the tank does not directly affect the time it takes to fill with water. However, it can indirectly affect the rate at which water is being added, which in turn will affect the time. A taller tank may have a higher rate of water being added compared to a shorter tank, resulting in a shorter time to fill.

## 5. Are there any other factors that can affect the time it takes to fill a tank with water?

Yes, there are other factors that can affect the time it takes to fill a tank with water. These include the size and shape of the tank, the pressure of the water being added, and any obstructions or blockages in the tank's inlet or outlet.

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