Fluid statics seems easy but can't figure it out .

[gikwiye]

Homework Statement

A cylindrical tank of internal diameter 1.5m and length 2.0m is mounted on a trailer. When the tank is filled with water the combined weight is 55 kN. Find the weight of tank plus trailer with the tank full of methyl alcohol (relative density 0.789).

Homework Equations

density*volume=mass
pi*r²*length= volume of cylindre

The Attempt at a Solution

total volume of methyl in tank= 3.53 m³
using density of methyl (789 kg/m³)
mass of methyl in tank= 2788.55 kg
however, I don't see how this is going to help finding the mass of water in the tank filled with water or the mass of the tank. Basically, if I don't find the volume of water in the tank filled but not fully with water I cannot find the mass of that water. Therefore, I cannot find the mass of the tank and trailer.
if anybody could help that would be nice.
thanks.

 

[Doc Al]

total volume of methyl in tank= 14.13 m³

How did you calculate that volume? (Is 1.5 m the radius or the diameter?)

however, I don't see how this is going to help finding the mass of water in the tank filled with water or the mass of the tank.

You can find the mass of the water just like you can find the mass of the methyl alcohol. You are given the total weight, so what's the total mass of truck plus water?

 

[gikwiye]

How did you calculate that volume? (Is 1.5 m the radius or the diameter?)

sorry made a mistake on that one.

You can find the mass of the water just like you can find the mass of the methyl alcohol. You are given the total weight, so what's the total mass of truck plus water?

no because the tank is not fully filled with water unless I know the volume I can't find it

 

[gikwiye]

tried it with the corrected value of r it still doesn't work ( forgot to tell the answer should be around 47.7kN

 

[Doc Al]

tried it with the corrected value of r it still doesn't work ( forgot to tell the answer should be around 47.7kN

Answer these questions:

What's the volume of the tank?

What's the mass of the water?

What's the total mass of the truck + water?

What's the mass of the truck alone (empty tank)?

What's the mass of the alcohol?

 

[gikwiye]

Answer these questions:

What's the volume of the tank?

What's the mass of the water?

What's the total mass of the truck + water?

What's the mass of the truck alone (empty tank)?

What's the mass of the alcohol?

1. 0.75²*pi*2=3.53m³
2.mass of water:( 55kN-weight of tank)/9.81
3. total mass of truck+water=55kN/9.81=5606.52 Kg
4.mass of empty tank= 5606.52 Kg-mass of water
5.mass of alcohol= 2785.17 Kg( in a tank full of alcohol)

note 2 and 3 are the same equations which leads to 0=0.
Moreover, I don't really see the point of the alcohol in this problem. In fact if we have a tank entirely filled with alcohol how is it related to the not entirely water filled tank?

 

[Doc Al]

1. 0.75²*pi*2=3.53m³

OK.

2.mass of water:( 55kN-weight of tank)/9.81

Figure it out using density X volume. What's the density of water?

3. total mass of truck+water=55kN/9.81=5606.52 Kg

OK.

4.mass of empty tank= 5606.52 Kg-mass of water

No. That's the total mass of truck + water. (See #3.) You'll need to combine the correct answer to #2 with #3 to solve for the mass of the empty truck.

5.mass of alcohol= 2785.17 Kg( in a tank full of alcohol)

Good. (Figure out the answer to #2 in the same way.)

 

[gikwiye]

OK.

Figure it out using density X volume. What's the density of water?

OK.

No. That's the total mass of truck + water. (See #3.) You'll need to combine the correct answer to #2 with #3 to solve for the mass of the empty truck.

Good. (Figure out the answer to #2 in the same way.)

ok here is what I did but did not get the right answer.

mass of water = density of water x volume of water in the tank= 1000(kg/m³)*3.53(m³)
=3530 kg note : I did this as if the tank was fully filled with water but it is not.
mass of tank= total mass ( tank + water) minus mass of water. you have then 5606.52kg-3530kg=2076.52kg for the mass of the tank.
In Newtons, you have 20.370 kN.
the answer should be 47.7 kN

 

[Cilabitaon]

ok here is what I did but did not get the right answer.

mass of water = density of water x volume of water in the tank= 1000(kg/m³)*3.53(m³)
=3530 kg note : I did this as if the tank was fully filled with water but it is not.

Yes, the question says "when the tank is filled with water" so you now have the correct mass of water.

mass of tank= total mass ( tank + water) minus mass of water. you have then 5606.52kg-3530kg=2076.52kg for the mass of the tank.

This is also correct, now you have the mass of an empty container, but what does the question ask for?

In Newtons, you have 20.370 kN.

This is the correct weight of the container, but read my last statement.

 

[gikwiye]

Yes, the question says "when the tank is filled with water" so you now have the correct mass of water.



This is also correct, now you have the mass of an empty container, but what does the question ask for?



This is the correct weight of the container, but read my last statement.

yeah the question says filled not "fully" filled and the question asks for the weight of the container. However, in this exercice I should find 47.7 kN for it's weight.

 

[Cilabitaon]

When the tank is filled with water the combined weight is 55 kN.

fill - occupy: occupy the whole of; "The liquid fills the container"

So when a question says 'filled you can assume it means to the containers capacity; after all I used this and got the correct answer(according to you).

Find the weight of tank plus trailer with the tank full of methyl alcohol (relative density 0.789).

So you have to do a bit of extra working; otherwise what would be the use of even mentioning the methanol at all?

 

[Doc Al]

mass of water = density of water x volume of water in the tank= 1000(kg/m³)*3.53(m³)
=3530 kg

Good.

note : I did this as if the tank was fully filled with water but it is not.

Sure it's full. You are told as much.

mass of tank= total mass ( tank + water) minus mass of water. you have then 5606.52kg-3530kg=2076.52kg for the mass of the tank.

Excellent.

In Newtons, you have 20.370 kN.
the answer should be 47.7 kN

You forgot to add the mass of the methyl alcohol.

 

[gikwiye]

yeah the question says filled not "fully" filled and the question asks for the weight of the container. However, in this exercice I should find 47.7 kN for it's weight.

thank you very much for your help I got it now. It is the way I read the question that was wrong. I'll try to be more focused next time. thanks again

 

[Cilabitaon]

thank you very much for your help I got it now. It is the way I read the question that was wrong. I'll try to be more focused next time. thanks again

Finally

Glad we could help.