Unit Conversion: What went wrong?

[xiangru119]

Homework Statement

Pressures up to 3000 atm are measured with a dead-weight gauge. The piston diameter is 0.17 (in). What is the approximate mass in (lbm) of the weights required?

The Attempt at a Solution

Abs. pressure = Gauge pressure + Atmospheric pressure
= 3000 atm + 1 atm
= 3001 atm * 14.696 psi/atm
= 44102.696 psi
A = pi*D2/4
= 0.023 in2
P = F/A
P*A = mg
44102.696*0.023 = m * 32.174 ft/s2 (12 in./1 ft)
m= 2.627 lbm

4. The actual answer: 1000.7 lbm. So can anyone point out my error?
Any help would be appreciated. Thank you.

 

[Dickfore]

A mass of 1 lbm weighs 1 lbf in standard gravitational field.

$$4.41 \times 10^{4} \, \frac{\mathrm{lb}}{\mathrm{in}^{2}} \times (2.3 \times 10^{-2} \, \mathrm{in}^{2}) = 1.01 \times 10^{3} \, \mathrm{lb}$$

 

[xiangru119]

A mass of 1 lbm weighs 1 lbf in standard gravitational field.

$$4.41 \times 10^{4} \, \frac{\mathrm{lb}}{\mathrm{in}^{2}} \times (2.3 \times 10^{-2} \, \mathrm{in}^{2}) = 1.01 \times 10^{3} \, \mathrm{lb}$$

Hi, the answer obtained from this should be equivalent to pound force. How about the accelerate force of gravity? Thanks for your comment.

 

[Dickfore]

Hi, the answer obtained from this should be equivalent to pound force. How about the accelerate force of gravity? Thanks for your comment.

I don't know what you are talking about. I was not supposed to solve even this much I think. Please use proper English to communicate your ideas.

 

[xiangru119]

I apologise for my broken English. I mean the answer obtained (1.01x10^3 lb) might be lbf instead of lbm. I think acceleration of gravity needed to be taken into account in order to get lbm.

 

[Dickfore]

But, it is taken into account. Did you read this:

A mass of 1 lbm weighs 1 lbf in standard gravitational field.

 

[xiangru119]

Ok, I will think about it. Thanks