| A short study was carried out to look deep into relation between two significant energy equations; the first law of thermodynamics and Bernoulli equation. The first law of thermodynamics was derived from a thermal cycle, so we can say that there is heat transfer and internal energy change. Bernoulli equation, in the other hand, was derived from Euller's equation, which is a mechanical energy derivation, and there is no heat transfer and internal energy change. If both equations are energy equations, then, we come up with an idea that there may be a relation. This paper presents the derivation in a determined way to show clearly that even though the first laws of thermodynamics and Bernoulli equation are derived from entirely different sources and with differently method, they end up identical form of energy equation. The first law of thermodynamics was derived first, and then reduces to Bernoulli equation by eliminating internal energy change and the rate of heat transfer. The procedure is not very complicate, it just a straight forward of solution with application of some restrictions or boundary conditions. The relation was studied by considering steady flow in the absence of shear forces in a control volume, the so called, streamtube, bounded by streamline along its periphery. Solving the first law of thermodynamics for this streamtube results an energy equation identical to Bernoulli equation with additional terms; internal energy change and the rate of heat transfer per unit mass. If this additional terms are set to be zero, the equation reduces to Bernoulli equation. Bernoulli equation is a mechanical energy balance with no conversion of mechanical to thermal energy. Finally, it was concluded that the first laws of thermodynamics and Bernoulli equation are absolutely two different equations, although there are some identical properties. |