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Fluid formulas

Master Fluid through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Fluid, every formula

22 formulas, typeset and free. Print it, or keep it open beside your practice.

Pressure
$P = \frac{F}{A}$
Pressure at depth
$P = P_{0} + ρ g h$
Pascal's law
$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$
Q1MCQPascal's law
A hydraulic press works on:
- A
  $\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}$
- B
  $F_1 A_1=F_2 A_2$
- C
  $F_1=F_2$
- D
  $A_1=A_2$
Density
$ρ = \frac{m}{V}$
Relative density
$RD = \frac{ρ}{ρ _{w a t er}}$
Q1MCQRelative density
Relative density is the ratio of a substance's density to that of:
- A
  water
- B
  air
- C
  mercury
- D
  vacuum
Archimedes' principle (buoyancy)
$F_{B} = ρ_{f l u i d} V_{s u b} g$
Q1MCQBuoyancy
The buoyant force on a submerged body is:
- A
  $\rho_{fluid}V_{sub}g$
- B
  $\rho_{body}Vg$
- C
  $\rho_{fluid}Vg^{2}$
- D
  $mg$
Law of floatation
$ρ_{b o d y} V g = ρ_{f l u i d} V_{s u b} g$
Q1MCQFloatation
A body floats when the weight of displaced fluid equals:
- A
  the weight of the body
- B
  twice the body's weight
- C
  zero
- D
  the buoyant force only
Equation of continuity
$A_{1} v_{1} = A_{2} v_{2}$
Bernoulli's equation
$P + \frac{1}{2} ρ v^{2} + ρ g h = constant$
Q1MCQBernoulli
Bernoulli's equation states that along a streamline:
- A
  $P+\tfrac12\rho v^{2}+\rho g h=\text{const}$
- B
  $P+\rho v=\text{const}$
- C
  $Pv=\text{const}$
- D
  $P+\rho g h=v$
Torricelli's theorem
$v = 2 g h$
Venturimeter flow
$v_{1} = A_{2} \frac{2 g h}{A _{1}^{2} - A _{2}^{2}}$
Q1MCQVenturimeter
A venturimeter measures:
- A
  the flow speed of a fluid
- B
  surface tension
- C
  viscosity
- D
  density only
Viscous force (Newton)
$F = η A \frac{d v}{d x}$
Q1MCQViscous force
Newton's viscous force is:
- A
  $\eta A\dfrac{dv}{dx}$
- B
  $\dfrac{\eta A}{dv/dx}$
- C
  $\eta v$
- D
  $6\pi\eta r v$
Stokes' law
$F = 6 π η r v$
Q1MCQStokes' law
The viscous drag on a small sphere is:
- A
  $6\pi\eta r v$
- B
  $\eta A\dfrac{dv}{dx}$
- C
  $\pi\eta r^{2}v$
- D
  $4\pi\eta r v$
Terminal velocity
$v_{t} = \frac{2 r ^{2} ( ρ - σ ) g}{9 η}$
Q1MCQTerminal velocity
The terminal velocity of a sphere in a fluid is:
- A
  $\dfrac{2r^{2}(\rho-\sigma)g}{9\eta}$
- B
  $\dfrac{9\eta}{2r^{2}g}$
- C
  $\sqrt{2gh}$
- D
  $6\pi\eta r$
Reynolds number
$R e = \frac{ρ v D}{η}$
Q1MCQReynolds number
The Reynolds number is:
- A
  $\dfrac{\rho v D}{\eta}$
- B
  $\dfrac{\eta}{\rho v D}$
- C
  $\rho v D\eta$
- D
  $\dfrac{v D}{\eta}$
Poiseuille's law
$Q = \frac{π P r ^{4}}{8 η L}$
Q1MCQPoiseuille
The volume flow rate through a tube is:
- A
  $\dfrac{\pi P r^{4}}{8\eta L}$
- B
  $\dfrac{\pi P r^{2}}{8\eta L}$
- C
  $\dfrac{8\eta L}{\pi P r^{4}}$
- D
  $\pi P r^{4}$
Surface tension
$T = \frac{F}{L}$
Q1MCQSurface tension
Surface tension is defined as force per unit:
- A
  length
- B
  area
- C
  volume
- D
  mass
Excess pressure (drop)
$Δ P = \frac{2 T}{r}$
Q1MCQExcess pressure (drop)
The excess pressure inside a liquid drop is:
- A
  $\dfrac{2T}{r}$
- B
  $\dfrac{4T}{r}$
- C
  $\dfrac{T}{r}$
- D
  $\dfrac{2T}{r^{2}}$
Excess pressure (bubble)
$Δ P = \frac{4 T}{r}$
Q1MCQExcess pressure (bubble)
The excess pressure inside a soap bubble is:
- A
  $\dfrac{4T}{r}$
- B
  $\dfrac{2T}{r}$
- C
  $\dfrac{T}{r}$
- D
  $\dfrac{8T}{r}$
Capillary rise
$h = \frac{2 T cos θ}{ρ g r}$
Q1MCQCapillary rise
The height of capillary rise is:
- A
  $\dfrac{2T\cos\theta}{\rho g r}$
- B
  $\dfrac{\rho g r}{2T\cos\theta}$
- C
  $\dfrac{2T}{r}$
- D
  $\dfrac{T\cos\theta}{\rho g}$
Surface energy
$E = T \times Δ A$
Q1MCQSurface energy
The surface energy is:
- A
  $T\times\Delta A$
- B
  $\dfrac{T}{\Delta A}$
- C
  $T$
- D
  $\dfrac{\Delta A}{T}$
Pressure energy (Bernoulli term)
$\frac{P}{ρ}$
Q1MCQBernoulli lift
An aeroplane wing generates lift because air moves:
- A
  faster over the top, lowering the pressure there
- B
  faster under the wing
- C
  equally on both sides
- D
  only downward

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Fluid formulas

Fluid, every formula

Pressure

Pressure at depth

Pascal's law

Density

Relative density

Archimedes' principle (buoyancy)

Law of floatation

Equation of continuity

Bernoulli's equation

Torricelli's theorem

Venturimeter flow

Viscous force (Newton)

Stokes' law

Terminal velocity

Reynolds number

Poiseuille's law

Surface tension

Excess pressure (drop)

Excess pressure (bubble)

Capillary rise

Surface energy

Pressure energy (Bernoulli term)

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