Pascal's law says that the:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 30-10-2020 (Evening)
Detailed Explanation
Blaise Pascal formulated this foundational law of hydrostatics in 1653, establishing that pressure in an equilibrium fluid element possesses no directional bias.
Consider a static fluid with no relative motion between adjacent fluid layers:
1. Absence of shear stress:
\[ \tau = \mu \frac{du}{dy} = 0 \]
2. Mohr's circle of stress for a static fluid element reduces to a single point on the normal stress axis because shear stress is zero on all planes.
3. Consequently, the normal stress (hydrostatic pressure) is identical in all directions:
\[ \sigma_x = \sigma_y = \sigma_z = -p \]
4. Therefore, pressure is a scalar quantity at a point, acting with equal intensity in all directions normal to any boundary.
Why “intensity of pressure at a point in a fluid at rest is equal in magnitude in all directions” Is Correct
Pascal's law applies specifically to a fluid at rest, stating that pressure intensity is identical in all directions. In a moving fluid with velocity gradients, viscous shear stresses cause normal stresses in different directions to deviate from each other.
Why the Other Options Are Wrong
- B. intensity of pressure at a point in a fluid at rest is equal to zero: Static fluid pressure is not zero; it equals the hydrostatic head ρgh plus surface pressure.
- C. intensity of pressure at a point in a fluid at rest cannot be determined: Fluid pressure is readily determined via manometers, barometers, or the hydrostatic equation p = ρgh.
- D. intensity of pressure at a point in a fluid at motion is equal in magnitude in all directions: In moving real fluids with velocity gradients, viscous stresses create directional differences in normal stresses.
Key Point
Pascal's law: At any point in a fluid at rest, pressure intensity is equal in all directions.
Key Concepts for Students
- Fluid pressure is a scalar quantity because it acts uniformly in all directions at a given point.
- The force exerted by fluid pressure on any surface always acts perpendicular (normal) to that surface.
- Pressure transmission without loss throughout a confined liquid enables hydraulic multiplication of force.
Practice more: this is question 13 in Hydrostatic Pressure MCQs – Part 1. Try the whole set and check every answer instantly.