Energy Analysis of Open System

Mass and Energy Analysis of Control Volumes

Mass Flow Rate:

It is defined as;

Amount of mass flowing through a cross-section per unit time.

The differential form of mass flow rate is given by:

Where, Vn is the normal, perpendicular velocity or Guassian velocity profile quotient and it tells us that at the walls of static pipe, velocity is zero and at the centre, velocity is maximum.

The normal velocity is given by using Guassian velocity profile quotient which depends upon:

Volume Flow Rate:

The volume of the fluid flowing through a cross-section per unit time is called Volume Flow Rate.

Relation between Mass and Volume Flow Rate:

The relation between Mass and Volume Flow Rate is given given below:

Conservation of Mass Principle or Mass Balance:

It states that:

Mass can neither be created nor be destroyed that is mass is a conserved quantity.

 The mass balance for an open systen is given by:

Mass Balance for steady flow process is given by:

Flow Work or Flow Energy:

Energy required for motion of fluid from one place to another. 

Total Energy of a Flowing Fluid:

Total energy of a flowing fluid is equal to the sum of internal, kinetic, potential and flow energies.

•°• h = u + PV 

Energy Balance for Steady Flow Process:

Energy balance for the steady flow process is:

And,

Steady Flow Devices:

Devices which act according to the properties which cannot change with time are called steady flow devices.

1. Nozzles:

Nozzle is a steady flow devices which increase ms the velocity of fluid at the expense of pressure.

Energy balance for the nozzle is given by:

Expanding the steady flow energy balance:

Since, for steady flow process 

Mass entering the system = Mass leaving the system 

Since, fluid does not stay in system for long, so there is no significant change in heat transfer, no work in and out and no change in potential energy.

Δ Q ⋍ 0

Δ W ⋍ 0

Δ P.E ⋍ 0

So, the above equation becomes:

2. Diffusers:

Diffusers is a steady flow devices which decreases the velocity but increases the pressure of the fluid.

Energy balance for the diffuser is given by:

Expanding the steady flow energy balance:

Since, for steady flow process

Mass entering the system = Mass leaving the system 

Since, fluid does not stay in system for long, so there is no significant change in heat transfer, no work in and out and no change in potential energy.

Δ Q ⋍ 0

Δ W ⋍ 0

Δ P.E ⋍ 0

So, the above equation becomes:

3. Throttling Valve:

It is a kind of flow restricting devices that cause a significant pressure drop in the fluid.

Energy balance for throttling valve is given by:

Expanding the steady flow energy balance:

Since, for steady flow process

Mass entering the system = Mass leaving the system 

Since, enthalpy remains constant, so throttling valve is also called Isenthalpic Devices.

4. Mixing Chambers:

Mixing chambers are devices where two streams of fluid at different temperatures mixed with each other.

Energy balance for mixing chambers is given by:

Mass Balance for mixing chambers is:

Mixing chambers are usually well-insulated, don't involve any kind of work and no changes in Kinetic and Potential Energies.

Δ Q ⋍ 0

Δ W ⋍ 0

Δ P.E ⋍ 0

Δ K.E ⋍ 0

So, energy balance becomes:

5. Heat Exchangers:

Heat exchangers are the devices in which two moving fluid streams exchange heat without mixing. It us also called Shell and Tube or Double Tube Heat Exchanger.

Energy balance for fluid A is given by:

Energy balance for fluid B is given by:

Energy balance for whole heat Exchanger if ( m1 = mA and m3 = mB ) is:

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