How many lbs. of water are in the tank?

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the weight of water in a tank that is 50% full. The tank has a total volume of 8000 gallons, and the density of water is given as 8.33 lbs/gallon. Participants explore the correct approach to calculating the mass of water based on the provided volume and density, while also addressing nuances in the units of measurement used in the U.S. system.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the calculation should be based on the volume of water, which is 4000 gallons, leading to a mass calculation of mass = volume x density = 4000 gallons x 8.33 lbs/gallon.
  • Others point out that the original calculation mistakenly used 8000 gallons instead of 4000 gallons, leading to confusion about the correct mass value.
  • A few participants discuss the distinction between pounds as a unit of force (lbf) and pounds as a unit of mass (lbm), noting that in the context of the problem, the density provided can be used directly without concern for the distinction.
  • Some participants emphasize the importance of double-checking arithmetic and ensuring that results are copied correctly, as errors in calculation have been noted.
  • There is a mention of the common usage of "pound" in the U.S. system, where it can refer to both mass and weight, which adds complexity to the discussion.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of units and the correct calculation method. While there is some consensus on the need to use 4000 gallons for the calculation, the discussion remains unresolved on the implications of using pounds as a unit of mass versus weight.

Contextual Notes

There are unresolved issues regarding the assumptions made about units of measurement and the implications of using density in the context of mass versus weight. The discussion highlights the potential for confusion in calculations due to these nuances.

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Homework Statement



2. A tank has a volume of 8000 gallons and is 50% full. If the tank contains water, which has a density of 8.33 lbs/gallon, how many lbs. of water are in the tank?

Homework Equations

The Attempt at a Solution


Volume occupied is 50% i.e 4000 gallons , given that the density is 8.33 lbs/gallons

Therefore, the mass occupied by water in lbs is given by
mass =volume x density = 8000gallon x 8.33/gallon33320

https://www.physicsforums.com/file:///C:/Users/Jim/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif
 
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jim1174 said:

Homework Statement



2. A tank has a volume of 8000 gallons and is 50% full. If the tank contains water, which has a density of 8.33 lbs/gallon, how many lbs. of water are in the tank?

Homework Equations

The Attempt at a Solution


Volume occupied is 50% i.e 4000 gallons , given that the density is 8.33 lbs/gallons

Therefore, the mass occupied by water in lbs is given by
mass =volume x density = 8000gallon x 8.33/gallon33320

https://www.physicsforums.com/file:///C:/Users/Jim/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif
What's your answer? The last thing you wrote was "8000gallon x 8.33/gallon33320", which makes no sense.
 
Last edited by a moderator:
jim1174 said:

Homework Statement



2. A tank has a volume of 8000 gallons and is 50% full. If the tank contains water, which has a density of 8.33 lbs/gallon, how many lbs. of water are in the tank?

Homework Equations

The Attempt at a Solution


Volume occupied is 50% i.e 4000 gallons , given that the density is 8.33 lbs/gallons

Therefore, the mass occupied by water in lbs is given by
mass =volume x density = 8000gallon x 8.33/gallon33320

https://www.physicsforums.com/file:///C:/Users/Jim/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif
well, in the US system of measure , lb or lbs is a force or weight unit, not a mass unit. Density is weight per unit volume. Weight is density x volume.
 
Last edited by a moderator:
In standard usage in the U.S. the term "pound" can denote either a unit of force or of mass. It is most commonly used in the sense of a mass. But that is irrelevant here. The problem states as a given that water has a density of 8.33 pounds per gallon. So for purposes of the problem we may safely assume that water has a density of 8.33 pounds per gallon. Whether that "8.33 pounds" is intended to denote the gravitational downforce on a gallon of water or is intended to denote the mass of a gallon of water will not change the numerical value of the intended answer to the problem and will not change the name of the unit of measure in which that result should be reported.

But we digress. Mark44's request for clarification is appropriate.
 
PhanthomJay said:
well, in the US system of measure , lb or lbs is a force or weight unit, not a mass unit. Density is weight per unit volume. Weight is density x volume.
As another guy who grew up with the US system, I can tell you that the clear implication is lbm (as indicated by jbriggs444).

Regarding the OPs calculation, he calculated 4000 gallons, but then still used 8000 gal in the mass calculation. Go figure.

Chet
 
Oh here we go again. A lb is a force unit, sometimes denoted lbf by those unfamiliar with US units. A pound of mass, which is used by virtually no one, is designated lbm. A gallon of water weighs 8.33 pounds in the US. No one cares that it has a mass of 8.33 lbm, not in the layman's world nor in the technical world. When mass must be used technically, we take its Earth weight in lbs and divide by 32 and don't give it a name, even though that mass unit is slugs.
 
is this the answer mass= volume*density= 4000gallon*8.33lb/gallon=3332
 
Last edited:
jim1174 said:
is this the answer mass= volume*density= 4000gallon*8.33lb/gallon=3332
No, it's not.

And the units of the answer would be lb.
 
jim1174 said:
is this the answer mass= volume*density= 4000gallon*8.33lb/gallon=3332

Always double check your arithmetic, and make sure you copy down results correctly. You multiplied 4000 by 8.33 and wound up with a number which was less than 4000.
 
  • #10
Volume occupied is 50% i.e. 4000 gallons, given that the density is 8.33 lbs/gallons

Therefore, the mass occupied by water in lbs is given by
mass =volume x density = 4000gallon x 8.33lbs/gallon=33320 lbs

Final Answer is = 33320 lbs
 

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