Q1: Equation of continuity of fluids is applicable only if

ANS:E - all the above.

1. Flow is Steady: Steady flow means that the flow conditions at any given point in the fluid do not change with time. In other words, the velocity, pressure, and other flow properties remain constant at any fixed point in the flow field over time. This condition allows us to use simplified mathematical models, such as the equation of continuity and the Bernoulli's equation, to analyze the flow behavior.
2. Flow is Compressive: Flow being compressive generally refers to situations where changes in pressure significantly affect the density of the fluid. For instance, compressive flow might occur in gases under high pressure conditions. However, in many fluid flow scenarios, especially in liquids like water, the compressibility effects are negligible, and the flow can be treated as incompressible. The compressibility of the fluid becomes important when analyzing flows at high speeds or under extreme pressure conditions.
3. Flow is One-Dimensional: One-dimensional flow means that flow variations occur primarily along one direction, typically the flow direction. While real-world flows are often three-dimensional, in many practical engineering applications, the variations in flow properties across the other dimensions (such as width and depth) are relatively small compared to the variations along the flow direction. This allows for the simplification of flow analysis by focusing on the predominant direction of flow.
4. Velocity is Uniform over the Cross-Sections: Uniform velocity means that the velocity of the fluid is the same at all points within a given cross-section of the flow. In many engineering applications, achieving perfectly uniform velocity across the entire cross-section is challenging due to factors like boundary conditions, surface roughness, and flow obstacles. However, in some idealized cases, such as fully developed laminar flow in a straight pipe, the velocity profile can be approximately uniform across the cross-section.