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Finite Volume Analysis: Selection of Control Surface or Surfaces

Control Surface and Control Volume

for Conservation of Energy for One Entry and One Exit

from Control Surface

where CS is the control surface CV is the control volume

P₁, P₂ are the pressures acting on the CS at 1 and 2 in lb/ft² or N/m²

V₁, V₂ are speeds of the fluid entering and exiting the control surface

in ft/sec or m/sec

Z₁, Z₂ are the elevations at stations 1 and 2 in ft or m

ρ is the density of the fluid in slugs/ft³ or kg/m³

h_P is the head added to the fluid by a pump in ft or m

h_T is the head extracted from the fluid by a turbine in ft or m

h_L is the head loss due to friction between stations 1 and 2 in ft or m

g is the acceleration of gravity in ft/sec² or m/sec²

P₁/ρg + V₁²/2g + z₁ + h_P ˗ h_T = P₂/ρg + V₂²/2g + z₂ + h_L (in ft or m)

Energy In + Change in Energy = Energy out + Loss of Energy