The Pascal law states that the liquid at rest applies pressure at a point is the same in all directions. This means that the pressure is there in spite of the direction. And it is present in the same direction and is having the same magnitude.

Pressure in a Fluid

The pressure in a fluid refers to the force exerted by the fluid per unit area at a given point. It is a scalar quantity and is measured in units of force per unit area, such as pascals (Pa) or pounds per square inch (psi).

Isotropic Pressure

In an ideal fluid, the pressure at a point is the same in all directions. This is known as isotropic pressure. It means that the pressure at a point is equal regardless of the direction in which it is measured. This is because an ideal fluid does not have any internal friction or viscosity, and its particles can move freely without any resistance.

Effects of Fluid Motion

When the fluid is moving, the pressure at a point will not be the same in all directions. This is because the motion of the fluid introduces velocity gradients and changes in momentum, resulting in variations in pressure.

Effects of Viscosity

When a fluid is viscous, it means that it has internal friction and resistance to flow. Viscosity causes the fluid to resist shear forces and results in the formation of velocity gradients within the fluid. Due to these velocity gradients, the pressure at a point in a viscous fluid will not be the same in all directions.

Viscous and Static Fluid

Even in the absence of fluid motion, if the fluid is viscous, the pressure at a point will not be isotropic. This is because viscosity creates internal friction within the fluid, leading to variations in pressure.

Inviscous and Moving Fluid

If the fluid is inviscid (non-viscous) but moving, the pressure at a point will still not be isotropic. The motion of the fluid creates variations in velocity, resulting in differences in pressure at different points.

Viscous and Moving Fluid

When a fluid is both viscous and moving, the pressure at a point will be different in different directions. Viscosity introduces internal friction and resistance to flow, while fluid motion creates velocity gradients. These factors combine to cause variations in pressure at a given point in different directions.

Therefore, the correct answer is option 'E' - the pressure at a point in a fluid will not be the same in all directions when the fluid is viscous and moving.