Bernoulli’s equation arises from the classic [[First Law of Thermodynamics|thermodynamics energy equation]] for incompressible flow: $\dot{Q}−\dot{W}=\dot{m}[u_2+\dfrac{p_2}{\rho}+gz_2+\dfrac{v_2^2}{2}−(u_1+\dfrac{p_1}{\rho}+gz_1+\dfrac{v_1^2}{2})] $ By taking [[Heat|heat]] rate, [[Work|work]], and [[Internal Energy|internal energy]] change as zero we arrive at Bernoulli’s equation for [[Fluid|fluid]] flow: $0=\dfrac{p_2}{\rho}+gz_2+\dfrac{v_2^2}{2}−(\dfrac{p_1}{\rho}+gz_1+\dfrac{v_1^2}{2})$ We can rewrite this equation into the classic form of Bernoulli’s equation: $p_1+\rho gz_1+\dfrac{1}{2}\rho v_1^2=p_2+\rho gz_2+\dfrac{1}{2}\rho v_2^2$ There are three important terms in Bernoulli’s Equation: - $p$: Static Pressure, associated with the [[Pressure|pressure]] of the fluid at rest. - $\rho gz$: Hydrostatic Pressure, associated with the weight of fluid at a given depth. - $\dfrac{1}{2}\rho v^2$: Dynamic Pressure, associated with the motion of the fluid.