S.L. Arsenjev

Physical-Technical Group

Dobroljubova Street, 2, 29, Pavlograd Town, Dnjepropetrovsk region, 51400 Ukraine

The modern form of the Saint-Venant − Wantzel formula for an outflow velocity of gas stream from flow element, system is presented. The taking into account of contact interaction of gas stream with the streamline surface in the form of the static head law has allowed finding the spatial-energy liaison in flow system. The

physically correct combination of mechanics of contact interaction and thermodynamics of fluid in one formula has allowed simultaneously to be liberated from the velocity coefficient and the discharge coefficient and also polytropic process. In the new form the formula has gained the key character for computation of parameters of motion and state of gas stream in the flow system.

**PACS:** 47.10.+g -- 47.60.+i: Flows in ducts, channels, nozzles, and conduits

**Nomenclature**

flow element cross-section area; gravity acceleration; general height of a fall; height of the running point at free fall; adiabatic exponent; general length of the flow element; pressure before inlet and after outlet

of the flow element respectively; static head along the fluid stream; gas constant of the given gas; thermodynamic temperature of gas before inlet into the flow element; outflow velocity (average in the outlet cross-section); maximum possible outflow velocity; weight density of fluid before the flow element inlet.

### Saint-Venant – Wantzel formula modern form Part 3