Energy Balance
Mechanical Systems

Upon studying this section, you should be familiar with the following:

Energy Balance for Mechanical Systems

Explanation:

Energy balances on mechanical systems, just as open system energy balances, are derived from the closed system energy balance. It is used for systems in which kinetic energy, potential energy, or shaft work are of prime importance.

Derivation:

closed system balance, splitting up the work terms:

ΔU + ΔEk + ΔEp = Q - Ws - Wflow
with
F(friction) = ΔU - Q
in combining we have,
ΔEk + ΔEp + F = -Wflow - Ws

Doing some rearranging, substituting the definitions of Wflow, Ek, and Ep, and then dividing by the mass flow rate, we get the desired equation.

ΔP/ρ + Δu2/2 + g*Δz + F-hat = - Ws-dot / m-dot

Mechanical System Energy Balance Equation:

ΔP/ρ + Δu2/2 + g*δz + F-hat = - Ws-dot / m-dot

A modified form of this equation, used for a frictionless (F=0) process with no moving parts (Ws=0), is called the Bernoulli equation.

Bernoulli equation:

ΔP/ρ + Δu2/2 + g*Δz = 0

ΔP = 0 if the inlet pressure is equal to the outlet pressure

Δu2 = 0 if the system doesn't change velocity

Δz = 0 if the system doesn't move vertically



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