Physics · Mechanical Properties Of Solids · NEET
In magnitude, yes. When a body is squeezed by a fluid, the internal restoring force per unit area (hydraulic stress) is equal in size to the hydraulic pressure P applied by the fluid. So we usually just write hydraulic stress = P. The word 'stress' points to the body's internal restoring response, while 'pressure' points to the external cause, but numerically they match at equilibrium.
The fluid pushes perpendicular (normal) to the surface at every point, and it pushes equally from all sides. Because the push is uniform in every direction, the body shrinks evenly, so its shape (geometry) stays the same and only its size (volume) decreases. This is the opposite of shearing stress, where a sideways force changes shape but not volume.
Under hydraulic compression the volume decreases, so ΔV is negative and volume strain ΔV/V is negative. In NEET numericals we usually take the magnitude |ΔV/V| when we compute bulk modulus, and the minus sign appears in the bulk modulus formula B = -P / (ΔV/V) to keep B positive.
No. Volume strain is a ratio of two volumes (change in volume divided by original volume), so the units cancel out completely. It is a pure number with no units and no dimensional formula. Hydraulic stress, however, does have units (pascal, Pa = N/m squared), the same as pressure.
Longitudinal stress acts along one direction (pulling or pushing along the length) and changes length. Hydraulic stress acts perpendicular to the surface from all directions at once and changes volume. Longitudinal stress uses Young's modulus; hydraulic stress uses bulk modulus.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Hydraulic stress = applied force / area = P, the hydraulic pressure. Its SI unit is pascal (Pa) or N/m squared.
Volume strain = ΔV / V, where ΔV is the change in volume and V is the original volume. It has no units.
Bulk modulus B. It is defined as B = hydraulic stress / volume strain = -P / (ΔV/V). The minus sign keeps B positive because ΔV is negative during compression.
No. Because the fluid presses equally from all sides, the body shrinks uniformly and keeps its original shape. Only its volume changes.
It is normally a compressive stress, since a fluid under high pressure squeezes the body inward on all sides, reducing its volume.
