The equation: H ?_in=H ?_out is frequently applied to a valve. Several assumptions are incorporated into the derivation of this equation. Which of the following is NOT one of these assumptions?
A. The system is operating at steady state.
B. The system is adiabatic.
C. The potential energies of the entering and exiting streams are equal to each other.
D. The system is at constant, uniform pressure throughout.
E. All of the above are necessary assumptions for the derivation of this equation.
A. Incorrect. This is assumed resulting in removal of the time dependent or time derivative terms.
B. Incorrect. The equation would contain a Q term if the valve wasn’t assumed adiabatic. Valves are not used to add or remove heat. When there is a significant temperature difference between the fluid and the surroundings, the pipes and valves can be insulated to for safety and to prevent process interference.
C. Incorrect. No height terms are present. Additionally, the valve would have to be extremely large to justify including potential energy terms.
D. Correct. Pressures can be—and probably are—different for the fluid entering the valve than for the fluid leaving. Remember that enthalpy includes pressure in its definition (U + PV)
E. Incorrect. One of these assumptions is not incorporated into the equation.
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