Understanding Energy per Unit Weight: Solving the Equation for Height

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SUMMARY

The discussion centers on the interpretation of equation 3-4, specifically regarding the term "energy per unit weight." The quantity γ (gamma) is defined as γ = ρ ⋅ g, where ρ represents fluid density and g is the acceleration due to gravity. The unit of γ is confirmed to be kg(m^-2)(s^-2), which corresponds to weight density rather than weight itself. The relationship P / γ = height is established, reinforcing the concept of energy per unit weight in fluid mechanics.

PREREQUISITES
  • Understanding of fluid mechanics concepts, particularly weight density.
  • Familiarity with the variables ρ (density) and g (acceleration due to gravity).
  • Knowledge of dimensional analysis to interpret physical equations.
  • Basic grasp of pressure (P) in fluid systems.
NEXT STEPS
  • Study the derivation of weight density in fluid mechanics.
  • Learn about the implications of energy per unit weight in hydrostatics.
  • Explore dimensional analysis techniques for verifying physical equations.
  • Investigate the applications of pressure and height relationships in fluid dynamics.
USEFUL FOR

Students and professionals in engineering, particularly those focusing on fluid mechanics, as well as educators teaching related subjects in physics and applied mathematics.

hotjohn
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Homework Statement


why the author said the equation 3-4 as energy per unit weight ?
as gamma = rho g , gamma has the unit of kg(m^-3)(ms^-2) = kg(m^-2)(s^-2) , gamma is clearly not weight ...

Homework Equations

The Attempt at a Solution

 

Attachments

  • 0024.PNG
    0024.PNG
    13 KB · Views: 472
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Beg your pardon?
 
hotjohn said:

Homework Statement


why the author said the equation 3-4 as energy per unit weight ?
as gamma = rho g , gamma has the unit of kg(m^-3)(ms^-2) = kg(m^-2)(s^-2) , gamma is clearly not weight ...

Homework Equations

The Attempt at a Solution

You'll have to supply some additional information about this equation 3-4, which is not included in your attachment.

The quantity γ = ρ ⋅ g is known as the weight density of the fluid, however.
 
hotjohn said:

Homework Statement


why the author said the equation 3-4 as energy per unit weight ?
as gamma = rho g , gamma has the unit of kg(m^-3)(ms^-2) = kg(m^-2)(s^-2) , gamma is clearly not weight ...

Homework Equations

The Attempt at a Solution

 

Attachments

  • 0025.PNG
    0025.PNG
    12 KB · Views: 636
SteamKing said:
You'll have to supply some additional information about this equation 3-4, which is not included in your attachment.

The quantity γ = ρ ⋅ g is known as the weight density of the fluid, however.
P / γ = height . right ? why is energy per unit weight ?
 
hotjohn said:
P / γ = height . right ? why is energy per unit weight ?
Work out the units on both sides of the equation.
 

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