Question

Euler’s equations of motions can be integrated when it is assumed that

1. The continuity equation is satisfied.
2. The fluid is incompressible.
3. A velocity potential exists and the density is constant.
4. The flow is rotational and incompressible. 

Answer 1

Correct Answer - Option 3 : A velocity potential exists and the density is constant.

​Explanation:

Euler's equation of motion:

Euler's equation for a 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 Newton's Second Law of Motion which states that if the external force is zero, linear momentum is conserved. The integration of the equation gives Bernoulli's equation in the form of energy per unit weight of the following 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., the mass density of the fluid is constant)
• A velocity potential exists.
• 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.

As there is no external force applied (Non-viscous flow), therefore linear momentum will be conserved.