Pascal's law states that pressure at any point in a fluid at rest has :
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2009
Detailed Explanation
Pascal's law is the foundational theorem of hydrostatics, demonstrating that in the absence of shear stresses, fluid pressure is an isotropic scalar state variable.
Consider static equilibrium of an infinitesimal element at point \((x,y,z)\):
\[ \sum F_x = 0, \quad \sum F_y = 0, \quad \sum F_z = 0 \]
Because the fluid is at rest:
\[ \tau_{xy} = \tau_{yx} = \tau_{yz} = \tau_{zy} = \tau_{zx} = \tau_{xz} = 0 \]
Resolving normal stresses along any inclined plane at angle \(\theta\):
\[ p_n = p_x = p_y = p_z = p \]
Hence, pressure intensity has the same magnitude in all directions.
Why “Same magnitude in all direction” Is Correct
Pascal's law explicitly asserts that static fluid pressure has no preferred orientation; its magnitude is identical regardless of the angle of the surface against which it acts.
Why the Other Options Are Wrong
- A. different magnitude in all directions: Different magnitudes in different directions occur in solid mechanics or in viscous fluids under dynamic shear flow.
- C. Zero magnitude in all direction: Fluid pressure at rest is non-zero, equal to atmospheric plus hydrostatic column pressure.
- D. None of the above: Option (b) is correct; 'None of the above' is incorrect.
Key Point
Pascal's law: Fluid pressure at a point in a static fluid has the same magnitude in all directions.
Key Concepts for Students
- Pressure acts normal to any surface placed in contact with the static fluid.
- Because pressure has magnitude but no unique spatial direction, it is a tensor of rank zero (scalar).
- In a gravitational field, pressure varies from point to point vertically, but at any single point it is isotropic.
Practice more: this is question 24 in Hydrostatic Pressure MCQs – Part 2. Try the whole set and check every answer instantly.