On the Derivation of Euler's Equation for the Motion of an Inviscid Fluid

1950 ◽  
Vol 18 (7) ◽  
pp. 467-467 ◽  
Author(s):  
S. Corrsin
Keyword(s):  
Inviscid Fluid ◽  
Euler’S Equation ◽  
Euler's Equation

Bernoulli’s equation

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Hydrostatic Pressure ◽  
Dynamic Pressure ◽  
Mechanical Energy ◽  
Constant Density ◽  
Inviscid Fluid ◽  
Dimensionless Numbers ◽  
Vertical Column ◽  
Bernoulli’S Equation ◽  
Euler’S Equation ◽  
Euler's Equation

In this chapter Newton’s second law of motion is used to derive Euler’s equation for the flow of an inviscid fluid along a streamline. For a fluid of constant density ρ‎ Euler’s equation can be integrated to yield Bernoulli’s equation: p + ρ‎gz′ + ρ‎V2 = pT which shows that the sum of the static pressure p, the hydrostatic pressure ρ‎gz and the dynamic pressure ρ‎V2/2 is equal to the total pressure pT. The combination p + ρ‎V2/2 is an important quantity known as the stagnation pressure. Each of the terms on the left-hand side of Bernoulli’s equation can be regarded as representing different forms of mechanical energy and also equivalent to the hydrostatic pressure due to a vertical column of liquid. The dynamic pressure can be thought of as measuring the intensity or strength of a flow and is frequently combined with other fluid and flow properties to produce non-dimensional (or dimensionless) numbers which characterise various aspects of fluid motion.

Euler's Equation and (p, r) Coordinates

1954 ◽  
Vol 38 (325) ◽  
pp. 172
Author(s):  
K. E. Bullen
Keyword(s):  
Euler’S Equation ◽  
Euler's Equation

An overview of methods for calculating the head of a rotodynamic impeller and their practical significance

2003 ◽  
Vol 217 (3) ◽  
pp. 221-232 ◽  
Author(s):  
S Yedidiah
Keyword(s):  
Subject Matter ◽  
Practical Significance ◽  
Euler’S Equation ◽  
Euler's Equation ◽  
The Subject

This paper explains why Euler's equation and the airfoil theory, while analytically correct, sometimes produce disappointing results. It also emphasizes the merits of a recently developed approach and demonstrates its usefulness in solving problems encountered in practice. The subject matter relates, directly, only to rotodynamic pumps. However, with proper modifications, it can be easily expanded to other fluids machines.

A Correlation between Aerofoil Theory and Euler's Equation for Calculating the Head of a Constant-Pitch Axial-Flow Inducer

1987 ◽  
Vol 201 (5) ◽  
pp. 357-363 ◽  
Author(s):  
S Yedidiah
Keyword(s):  
Axial Flow ◽  
Impeller Blade ◽  
Euler’S Equation ◽  
Constant Pitch ◽  
Euler's Equation

This study indicates that the aerofoil theory of an impeller blade is not interchangeable with Euler's equation. Instead, these two approaches are supplementary to each other. The conclusion is well supported by observations from practice.

On Darboux solutions of the Euler's equation

1989 ◽  
Vol 37 (2-3) ◽  
pp. 279-281
Author(s):  
J. Smítal
Keyword(s):  
Euler’S Equation ◽  
Euler's Equation

Editorial-The Proof of Euler's Equation

1948 ◽  
Vol 55 (2) ◽  
pp. 94 ◽  
Author(s):  
C. B. Allendoerfer
Keyword(s):  
Euler’S Equation ◽  
Euler's Equation

Solitons, Euler’s equation, and vortex patch dynamics

1992 ◽  
Vol 69 (4) ◽  
pp. 555-558 ◽  
Author(s):  
Raymond E. Goldstein ◽  
Dean M. Petrich
Keyword(s):  
Patch Dynamics ◽  
Vortex Patch ◽  
Euler’S Equation ◽  
Euler's Equation
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