Answer to Question #154741 in Math for usman

Question

Name the different forces present in a fluid flow. For the Euler's equation of motion, which forces are taken into consideration

Answer 1

The important forces present in a moving liquid are Inertia Force, Viscous Force, Gravity Force, Surface Tension Force, Pressure Force and Elastic Force.

(a) Inertia force: It is the product of mass and acceleration of the flowing liquid.

(b) Viscous force: It is the product of shear stress due to viscosity and the cross-sectional area of flow.

(c) Gravity force: It is the product of mass and acceleration due to gravity of a flowing liquid.

(d) Surface tension force: It is the product of surface tension per unit length and length of the surface of flowing liquid.

(e) Pressure force: It is the product of intensity of pressure and the area of a flowing liquid.

(f) Elastic force: It is the product of elastic stress and the area of a flowing liquid.

The Euler's equation for steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure and density of a moving fluid.

It is based on the following assumptions:

The fluid is non-viscous (i,e., the frictional losses are zero).

The fluid is homogeneous and incompressible (i.e., mass density of the fluid is constant).

The flow is continuous, steady and along the streamline.

The velocity of the flow is uniform over the section.

No energy or force (except gravity and pressure forces) is involved in the flow.

Hence  for the Euler's equation of motion, only gravity and pressure forces are taken into consideration.