Bernoulli's equation is not applicable, when the flow is

Solution (By Examveda Team)

Imagine water flowing through a pipe. Bernoulli's equation is like a special tool that helps us understand how the pressure, speed, and height of the water are related. It's essentially a way to track the energy of the fluid as it moves.

But like any tool, Bernoulli's equation works best under certain "ideal" or "perfect" conditions. Think of it as assuming the fluid is "perfect" in some ways.

Here are the main ideal conditions (assumptions) for the most common form of Bernoulli's equation:

1. Incompressible: This means the fluid's density doesn't change. For example, water is usually considered incompressible because you can't easily squeeze it to make it denser.
2. Inviscid (Non-viscous): This is super important! Viscosity is like the "stickiness" or "internal friction" of a fluid. Honey is very viscous; water is much less viscous. An inviscid fluid has no friction at all. Bernoulli's equation, in its basic form, assumes there are no energy losses due to friction within the fluid itself or between the fluid and the pipe walls.
3. Steady Flow: This means the fluid's properties (like speed, pressure) at any point don't change over time.
4. Irrotational: This means that tiny fluid particles don't spin or rotate as they move along. They just move in a path without spinning.

Now let's look at the options and see when Bernoulli's equation is NOT applicable:

* Option A: Irrotational - Bernoulli's equation is applicable for irrotational flow. This is one of its ideal conditions, so it works fine here.
* Option B: Incompressible - Bernoulli's equation is applicable for incompressible flow. This is another key ideal condition, so it works fine here too.
* Option C: Viscous - Ah, here's the catch! If the flow is viscous, it means there's internal friction within the fluid. This friction causes energy to be lost (usually converted into heat). The basic Bernoulli's equation does not account for these energy losses. Therefore, it is not applicable in its simple form when the flow is viscous. You would need to add extra terms (like "head loss") to account for viscosity if you want to use a modified Bernoulli equation.
* Option D: All of the above - Since Bernoulli's equation *is* applicable for irrotational and incompressible flows, this option is incorrect.

So, the reason Bernoulli's equation is not applicable in its basic form is when the flow is Viscous because viscosity leads to energy losses that the basic equation doesn't include.

The correct answer is C: Viscous.