Mechanical properties of fluids

What you will understand

For NEET UG students: choose a pressure reference for water at rest, use continuity before calculating flow pressure, and identify when the ideal Bernoulli model applies. The worked examples keep depth, area, speed and pressure from becoming interchangeable shortcuts.

Jump to chapter practice →

Quick answer: first decide whether the fluid is at rest

For a constant-density liquid at rest in uniform gravity, $p_\mathrm{abs}=p_\mathrm{surface}+\rho gh$, with $h$ measured downward from the free surface. Gauge pressure is $p_\mathrm{abs}-p_\mathrm{atm}$; it equals $\rho gh$ when the surface is at that same atmospheric pressure.

For steady incompressible flow in a filled tube with no leaks, continuity gives $A_1v_1=A_2v_2$ using mean section speeds. Under a one-dimensional ideal-flow model with uniform section speeds, negligible viscosity, no pump or energy loss and points on the same streamline, use $p+\tfrac12\rho v^2+\rho gy=\text{constant}$. Use one consistent pressure reference.

Compare pressure at equal depths, not equal branch widths

Open full-size diagram ↗

Pressure is not force, and a pressure difference needs a cause

Pressure is a scalar; the pressure force on a surface element acts normally to that surface. For uniform pressure on a flat area, its normal force magnitude is $pA$, so equal pressure does not mean equal force on different areas. Hydrostatic buoyancy is the net result of pressure forces; for a displaced volume $V$ in a constant-density liquid, its upward magnitude is $\rho gV$.

In an ideal confined liquid at rest, an imposed pressure change is transmitted throughout the liquid. Account for height differences when comparing pressures. In flow, do not use “faster means lower pressure” without the streamline, height and energy assumptions.

Use continuity before Bernoulli

Open full-size diagram ↗

Switch models when viscosity or an interface matters

Viscosity describes resistance to shear flow and has unit Pa s; it can produce mechanical-energy losses that the simple Bernoulli equation above omits. Surface tension is force per unit length, with unit N/m; curved interfaces can create pressure jumps. A flat free-surface hydrostatic example does not supply a universal rule for droplets, bubbles or capillary tubes. Choose the model from the conditions stated in the question.

Common mistakes to catch

Do not report gauge pressure as absolute pressure or add atmospheric pressure twice. Equal depths in the stated connected static liquid give equal pressure, regardless of branch width. In a tube, area and diameter are different: a doubled circular diameter gives four times the area. The ideal-flow pressure difference includes the gravitational term if heights differ, and a real pump or viscous loss changes the balance.

Try it yourself 1: choose the pressure reference

In the water-at-rest example, surface pressure is 100 kPa and the depth contribution is 20 kPa. What is the absolute pressure? A. 20 kPa; B. 100 kPa; C. 120 kPa.

Try it yourself 2: apply continuity before guessing pressure

In the horizontal ideal-flow example, the area changes from 4 cm² to 2 cm². The initial speed is 2 m/s and static pressure 140 kPa. Which result follows? A. 4 m/s and 134 kPa; B. 1 m/s and 146 kPa; C. 4 m/s and 140 kPa.

A useful check on your next visit

Cover the diagrams and distinguish gauge from absolute pressure, then explain why the narrower flow section carries the same volume per second. Before each question, write “at rest” or “flowing” and state the pressure reference and assumptions.

Choose your next chapter task

Explain the distinction you missed, then apply it to a fresh chapter question.

Return to chapter practice and quiz choices →

Sources and review

Technical review: Codex (automated). Primary textbook sources checked on 23 October 2026. Diagrams, numerical examples and self-checks are original teaching material. Human subject review is not claimed.