S.L. Arsenjev , Y.P. Sirik

Physical-Technical Group

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

Solution of Euler momentum conservation equation for the real fluid - gas and liquid - stream in a pipe flow element is for the first time obtained on the basis of in essence new physically adequate approach to a problem on a contact interaction of the fluid with bodies. The flow element, system is: pipe, tube, mouthpiece, diffuser, etc. and its combination. Integration of the differential equation has led to the distribution law of static pressure along the flow element and one has proved the elementaryalgebraic solution, obtained in previous article by one of these authors [1]. But in contrast to previous solution, the integral solution allows to describe the real fluid motion under non-stationary conditions in combination with action of any time- varying physical factors: a pressure drop, applied to the fluid stream in the flow element, roughness of its wall, its cross-section area, and also the heat exchange with the streamlined surface, technical work, additional flow rate.

**PACS:** 01.40.Fk; 01.55.+b; 01.65.+g; 01.70.+w; 05.65.+b; 07.20.Pe; 47.60.+I; 47.85.-g

**Nomenclature**

internal diameter of the flow element; gravity acceleration; general height of free fall; height of running point at free fall; general metric length of the flow element; general caliber length of the flow element, L/D; metric length of stream from the outlet section of the flow element up to running point; pressure at inlet and at outlet of the flow element respectively; static pressure along the fluid stream; a stream velocity, determined by weight flow; weight density of fluid; coefficient of local hydraulic resistance for inlet into the flow element; coefficient of local hydraulic resistance for outlet from the flow element; coefficient of local hydraulic resistance within the limits of the flow element; hydraulic friction – Darcy -- coefficient.

### Modern fluid motion physics the Euler momentum conservation equation solution Part 2