Question

What is the General Equation? Explain the variables and parts of the equation. How is the GEneral Energy Equation applies to Water PUmps?

Answer 1

Solution:

According to 1st law of thermodynamic energy cant be created nor be destroyed but it can be transform from one form to another form.This is the basic law which deal with fluid as Genral energy equation for fluid.

The following is an analysis of the First Law of Thermodynamics to yield a general energy equation for fluids.

Energy transfers are denoted by:

Q = Transfer by Heat (J)

W = Transfer by Work (J)

q = Specific Transfer by Heat (J/kg)

w = Specific Transfer by Work (J/kg)

Qt = Transfer by Heat per Second, or Power (J/s = Watts)

Wt = Transfer by Work per Second, or Power (J/s = Watts)

Internal Energies and Enthalpies are denoted by:

U = Internal Energy (J)

u = Specific Internal Energy (J/kg)

H = U + PV = Enthalpy (J/K)

h = u + Pv = Specific Enthalpy (J/kg.K)

mt = mass flow rate (kg/s)

Note- Pump is our control system.

Under steady flow and a control volume, the First Law of Thermodynamics can be expressed as:

Qt + Wt =out mt*(h+v^2/2+gz) -in mt*(h+v^2/2+gz)

That is, in steady flow, the net rate of energy transfer to a control volume by heat and work transfer is equal to the difference between the rates of outgoing and ingoing energy flows by mass flow.In most cases, only one inlet and one outlet exist, so that the mass flow rate in is the same as the mass flow rate out. The First Law then reduces to:

Qt + Wt = mt*((h2-h1)+(V2^2/-V1^2)/2+g(z2-z1))

By dividing through by the mass flow rate, the equation can be rewritten in terms of specific values as:

q + w =h2-h1 +(V2^2-V1^2)/2+g(z2-z1)

Now, by noting that enthalpy, h, is defined as h = u + Pv = u+P/ρ and substituting and rearranging we get:

w+P1/1+V1^2/2+gz1=P2/2 +V^2/2+gz2+(u2-u1-q)

Now, the terms on the right hand side, u₂ - u₁ - q, represents the mechanical energy loss in the system. We can therefore define:

e_loss = u₂ - u₁ - q

By noticing that work is transferred in to a system through pumps,, we can rewrite the equation as:

P1/1+V1^1/2+gz1+wpump=P2/2+V2^2/2+gz2+eloss

By multiplying through my the mass flow rate, we arrive at the general energy formula for fluids:

mt*(P1/1+V1^2/2+gz1)+Wpump=mt*(P2/2+V2^2/2+gz2)+Eloss

thus Wpump=mt*(P2/2-P1/1+(V2^2-V1^2)/2+g*(z2-z1))+Eloss

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