Bulk modulus given, find change in P [Fluid Mechanics]

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Discussion Overview

The discussion revolves around calculating the change in pressure required to reduce the volume of water by 0.3%, given its bulk modulus at a specific temperature. The focus is on the application of fluid mechanics principles and the correct use of units in calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem and their initial calculation, stating that the change in pressure (dP) is 0.957 kip, but questions the use of US customary dimensions for pressure.
  • Another participant points out that pounds indicate force rather than pressure, which should be expressed in psi or ksi, and suggests rearranging the equation to ensure the units are correct.
  • A participant expresses confusion about consistently obtaining units of force instead of pressure and questions if the answer could be 957 psi.
  • A later reply confirms that the answer is indeed 957 psi.
  • One participant expresses gratitude for the assistance received in the discussion.

Areas of Agreement / Disagreement

There appears to be a consensus on the need to use the correct units for pressure, but uncertainty remains regarding the initial calculations and the final answer, as participants are still discussing the implications of their findings.

Contextual Notes

Participants highlight the importance of unit conversion and the implications of using force units instead of pressure units, indicating potential limitations in understanding the problem's requirements.

leafjerky
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Homework Statement


If the bulk modulus for water at
70∘F is 319 kip/in^2, determine the change in pressure required to reduce its volume by 0.3%.

Homework Equations


E = dP/(dV/V)
E - Bulk Modulus
dP - change in pressure
dV - change in volume
V - volume

The Attempt at a Solution


Well I just said 319 kip/in^2 = dP/(.003/1 in^2) so then dP = .957 kip or 957 lb. But it's looking for an answer using US customary dimensions for pressure. Any ideas? What did I overlook?
 
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leafjerky said:

Homework Statement


If the bulk modulus for water at
70∘F is 319 kip/in^2, determine the change in pressure required to reduce its volume by 0.3%.

Homework Equations


E = dP/(dV/V)
E - Bulk Modulus
dP - change in pressure
dV - change in volume
V - volume

The Attempt at a Solution


Well I just said 319 kip/in^2 = dP/(.003/1 in^2) so then dP = .957 kip or 957 lb. But it's looking for an answer using US customary dimensions for pressure. Any ideas? What did I overlook?
First of all, units of pounds indicate force, rather than pressure in USCS, which are given in pounds per square inch, or psi, usually.

Since the volume of the sample is reduced by 0.3%, a pure number without units, then re-arranging the original equation thus:

##E = \frac{dP}{dV/V}##

##E ⋅ (dV/V) = dP##

should result in units of pressure, whether they be ksi (= kip / in2) or psi, by suitable conversion.
 
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SteamKing said:
First of all, units of pounds indicate force, rather than pressure in USCS, which are given in pounds per square inch, or psi, usually.

Since the volume of the sample is reduced by 0.3%, a pure number without units, then re-arranging the original equation thus:

##E = \frac{dP}{dV/V}##

##E ⋅ (dV/V) = dP##

should result in units of pressure, whether they be ksi (= kip / in2) or psi, by suitable conversion.

I figured it should be, but for some reason I kept getting it as just lb or kip. So would the answer be 957 psi? I only have one attempt left.
 
leafjerky said:
I figured it should be, but for some reason I kept getting it as just lb or kip. So would the answer be 957 psi? I only have one attempt left.
Yes.
 
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Just wanted to say thanks SteamKing for being so helpful, you've answered stuff for me before.
 
You're welcome.
 

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