NDA Physics · Formula sheet

Fluid Mechanics and Properties of Matter formulas

10 formulas and 12 common traps for NDA Physics Fluid Mechanics and Properties of Matter, grouped by subtopic.

Pressure and Surface Tension

Pressure — force spread over an area

Pressure

P = \dfrac{F}{A}

$P$ pressure (Pa = N/m²)
$F$ force normal to the surface (N)
$A$ area over which the force acts (m²)

Pressure in a liquid — P = rho g h

Pressure due to a liquid column

P = \rho g h

$P$ gauge pressure at depth h (Pa)
$\rho$ density of the liquid (kg/m³)
$g$ acceleration due to gravity (m/s²)
$h$ depth below the free surface (m)

Pascal's principle — the hydraulic press

Hydraulic press

\dfrac{F_1}{A_1} = \dfrac{F_2}{A_2}

$F_1$ force on the small piston (N)
$A_1$ area of the small piston (m²)
$F_2$ force on the large piston (N)
$A_2$ area of the large piston (m²)

Atmospheric pressure, gauge vs absolute, and the pascal

Absolute pressure in a liquid open to air

P_{\text{abs}} = P_{\text{atm}} + \rho g h

$P_{\text{abs}}$ absolute (true) pressure (Pa)
$P_{\text{atm}}$ atmospheric pressure (Pa)
$\rho g h$ gauge pressure due to the liquid column (Pa)

Surface tension — the skin of a liquid

Surface tension

T = \dfrac{F}{L}

$T$ surface tension (N/m)
$F$ force along the surface (N)
$L$ length over which the force acts (m)

Common traps

Pressure rises when area shrinks

For a fixed force, P is inversely proportional to A. Resting a block on its SMALLEST face gives the GREATEST pressure. A common slip is to think the largest face presses hardest — it presses softest, because the same weight is spread over more area.

Pressure is NOT the same at all points

A frequent statement-MCQ trap claims 'pressure is the same at all points in a fluid at rest.' False — pressure is equal only at the same horizontal LEVEL; it grows with depth. What IS true: pressure exists everywhere in the fluid and presses on the walls.

Shape and base area do not matter

The hydrostatic paradox: a thin tall column and a wide shallow tank filled to the same height give the same pressure at the base. Only depth and density count, not the volume or the container shape.

Force is multiplied, energy is not

The hydraulic press gains force but loses distance — the big piston moves a smaller distance than the small piston, so work in equals work out. Do not claim it 'creates' energy. It only redistributes force and displacement.

Barometer vs manometer vs thermometer

A barometer measures ATMOSPHERIC pressure. A manometer measures the pressure of an enclosed gas. A thermometer measures temperature. The bank often lists all three as distractors — pick the barometer for atmospheric pressure.

Temperature LOWERS surface tension

The bank tests this directly. A tempting wrong option says surface tension 'increases with temperature' — it does the opposite. More heat means weaker surface attraction, so surface tension falls (and vanishes at the critical temperature).

Buoyancy, Density and Flotation

Learn this subtopic in the notes

Density and relative density

\rho = \dfrac{m}{V}, \qquad \text{RD} = \dfrac{\rho_{\text{substance}}}{\rho_{\text{water}}}

$\rho$ density (kg/m³)
$m$ mass (kg)
$V$ volume (m³)
$\text{RD}$ relative density (no unit)

Combining densities — equal volumes vs equal masses

Mixture density (equal masses)

\rho_{\text{eq.mass}} = \dfrac{2\rho_1\rho_2}{\rho_1 + \rho_2}

$\rho_1, \rho_2$ densities of the two components
$\rho_{\text{eq.mass}}$ density of an equal-mass mixture

Archimedes' principle and the buoyant force

Buoyant force (Archimedes)

F_b = \rho_{\text{fluid}}\, V_{\text{disp}}\, g

$F_b$ buoyant force / upthrust (N)
$\rho_{\text{fluid}}$ density of the fluid (kg/m³)
$V_{\text{disp}}$ volume of fluid displaced (m³)
$g$ acceleration due to gravity (m/s²)

Apparent weight loss on submersion

Apparent weight in a fluid

W_{\text{app}} = W - F_b

$W_{\text{app}}$ apparent (scale) weight in the fluid (N)
$W$ true weight in air (N)
$F_b$ buoyant force = weight of displaced fluid (N)

Float or sink — the density comparison

Fraction submerged of a floating body

\dfrac{V_{\text{submerged}}}{V_{\text{total}}} = \dfrac{\rho_{\text{body}}}{\rho_{\text{fluid}}}

$V_{\text{submerged}}$ submerged volume (m³)
$V_{\text{total}}$ total volume of the body (m³)
$\rho_{\text{body}}$ average density of the body
$\rho_{\text{fluid}}$ density of the fluid

Common traps

Relative density has no unit

RD is a ratio of two densities, so the units cancel — it is a pure number. An option that quotes RD 'in kg/m³' is wrong. Also remember water peaks in density near 4 °C, not at 0 °C.

Equal volumes vs equal masses give DIFFERENT averages

Equal volumes means the simple average (rho1+rho2)/2. Equal masses means 2 rho1 rho2 / (rho1+rho2), which is smaller. Read the question carefully — using the wrong one is the classic mistake on this HARD favourite.

Upthrust = weight of displaced FLUID, not of the body

The buoyant force depends on the fluid's density and the displaced volume — never on the body's own mass or weight. An option claiming the upthrust equals 'the mass of the body' is wrong on two counts: it is the fluid's weight, and a mass is not a force.

Mass is unchanged; only apparent weight drops

A submerged body does not lose mass or true weight — it only reads lighter on a scale because of the upthrust. The 'loss of weight' is exactly the buoyant force, equal to the weight of the displaced fluid.

It is AVERAGE density that decides flotation

Iron sinks, yet an iron ship floats — because the hull traps air and lowers the SHIP's average density below water's. Never reason from the material alone; compare the body's average density with the fluid's.

Stability is about M above G, not G below B

The trap options compare the centre of gravity with the centre of BUOYANCY. Stability is actually decided by the METACENTRE: M must be above G. A floating body can have G above B and still be perfectly stable.

Fluid Mechanics and Properties of Matter formulas

Pressure and Surface Tension

Pressure — force spread over an area

Pressure in a liquid — P = rho g h

Pascal's principle — the hydraulic press

Atmospheric pressure, gauge vs absolute, and the pascal

Surface tension — the skin of a liquid

Common traps

Buoyancy, Density and Flotation

Combining densities — equal volumes vs equal masses

Archimedes' principle and the buoyant force

Apparent weight loss on submersion

Float or sink — the density comparison

Common traps

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