Lecture 2 :Basic Modeling, Lecture notes of Engineering Science and Technology

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BASIC MODELING

Case 1

Any fluid is flowing at a rate of F1 into the

tank and flowing out at the rate of F2 ,as the

fluid varies with time.model the expression for

the fluid level in the tank at time t.

NATURAL MODEL

CAUSE AND EFFECT

RELATIONSHIP

Case 3

consider the inflow F1 passes through a fixed inlet valve from a pressure source P1. and flowing out at the rate of F2.The pressure on the downstream side of the inlet valve is P2,that is, the hydrostatic pressure in the tank at the level of the valve.in a similar fashion the outflow passes through a fixed valve with the hydrostatic pressure P on the upstream side discharging pressure P3.vessel is wholly enclosed and the pressure P 0 above the surface becomes a variable instead of constant.V 0 is the total volume of the tank Assumptions: Ideal gas Isothermal expansion and compression will be made. Temperature of gas remain constant and vaporization from the surface will be neglected.

• (^) Case 4 As continuation of case 3 assumed gas volume compresses under isothermal conditions.
  • (^) Adiabatic compression
  • (^) In adiabatic case all heat equivalent of the work done on/by the gas will appear as sensible heat

Case 5 Consider a well-agitated vessel with known flows in and outlet F 1 and F 2 .the inlet and outlet flows consist of a solvent that contains two soluble components,A & B.the inlet concentrations are CA1 & CB2.

Case 6. As continuation of case 5 suppose that components A and B react in the vessel, the reaction being defined as The effluent and vessel contents contain four components A,B,C and Develop the model.