ChE Fundamentals ISSUES!

My first assignment in chemical engineering basics class, and already I am having the problems!

1. Homework Statement

A horizontal cylindrical drum is 2m in diameter and 4m long. The drum is slowly filled with benzene (density = 0.879g/cm^3). Derive a formula for W, the weight in newtons of the benzene in the tank, as a function of h, the depth of the liquid in centimeters.

2. Homework Equations

We were not given any specific equations, but from attemting to do the solving I use:

Density = m/V
W=ma=mg
V=(pi)r^2h

3. The Attempt at a Solution

I have brainstormed. The volume of the drum is 4(pi)=12.56637. I believe that the problem wants for us to use W(h)=?? when finding the equation, and I understand we want to see that as the benzene increases the container becomes heavier. Also, we have the density.

Density = (m/V)
and W=mg, so W=V(density)g

We could plug things in.

W=(0.879)(9.8)V and get W=(8.7906)V

But here is where Im stuck. Does W=(8.7906)V equal W(h)? And should this be a relationship w/time since the benzene is flowing into the drum? I know this could include related rates (calculus) somewhere, but not sure where. Also, where does the drum's volume come in?

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Gokul43201
Staff Emeritus
Gold Member
My first assignment in chemical engineering basics class, and already I am having the problems!

1. Homework Statement

A horizontal cylindrical drum is 2m in diameter and 4m long. The drum is slowly filled with benzene (density = 0.879g/cm^3). Derive a formula for W, the weight in newtons of the benzene in the tank, as a function of h, the depth of the liquid in centimeters.

2. Homework Equations

We were not given any specific equations, but from attemting to do the solving I use:

Density = m/V
W=ma=mg
V=(pi)r^2h
Note the last equation you wrote above.

3. The Attempt at a Solution

I have brainstormed. The volume of the drum is 4(pi)=12.56637. I believe that the problem wants for us to use W(h)=?? when finding the equation, and I understand we want to see that as the benzene increases the container becomes heavier. Also, we have the density.

Density = (m/V)
and W=mg, so W=V(density)g

We could plug things in.

W=(0.879)(9.8)V and get W=(8.7906)V

But here is where Im stuck. Does W=(8.7906)V equal W(h)? And should this be a relationship w/time since the benzene is flowing into the drum? I know this could include related rates (calculus) somewhere, but not sure where. Also, where does the drum's volume come in?
You're nearly done. You just need to plug in the equation for the volume of the benzene in the drum.

PS: No, this has nothing to do with time, since you don't know the rate at which benzene is delivered to the drum.

Thank you very so much! It seems I have done some overthinking. I will do that!