Consider the following assumptions:1. The fluid is compressible2. The ...
Answer:
The Euler's equation of motion is a fundamental equation in fluid mechanics that describes the motion of a fluid. It is derived from the Navier-Stokes equations under certain assumptions. In order to apply the Euler's equation, we need to make some assumptions about the fluid.
The given assumptions are as follows:
1. The fluid is compressible.
2. The fluid is inviscid.
3. The fluid is incompressible and homogeneous.
4. The fluid is viscous and compressible.
Now, let's analyze each assumption and determine which ones are required for the Euler's equation.
Assumption 1: The fluid is compressible.
This assumption implies that the density of the fluid can change. The Euler's equation can be applied to both compressible and incompressible fluids, so this assumption is not required for the Euler's equation.
Assumption 2: The fluid is inviscid.
This assumption implies that the fluid has zero viscosity, which means there is no internal friction in the fluid. The Euler's equation is derived under the assumption of inviscid flow, so this assumption is required for the Euler's equation.
Assumption 3: The fluid is incompressible and homogeneous.
This assumption implies that the density of the fluid is constant and the fluid properties are the same at every point. The Euler's equation can be applied to both compressible and incompressible fluids, so this assumption is not required for the Euler's equation.
Assumption 4: The fluid is viscous and compressible.
This assumption implies that the fluid has viscosity and its density can change. The Euler's equation is derived under the assumption of inviscid flow, so this assumption is not required for the Euler's equation.
Conclusion:
From the above analysis, we can conclude that the assumptions required for the Euler's equation are:
- The fluid is inviscid.
- The fluid is incompressible and homogeneous.
Therefore, the correct answer is option 'B': 2 and 3.
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