Mechanical Properties of Fluids formulas
Class 11 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 9, the special cases questions are built on, and diagrams where they help.
By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE
Most used formulasOther formulas and cases
1Pressure and hydrostatics
Same at the same level in a connected liquid at rest; independent of vessel shape (hydrostatic paradox). Force on the base $=\rho ghA$, may differ from liquid weight. Barometer: $h=\dfrac{P_0}{\rho g}$ (10.3 m of water).
| Case | Result |
|---|---|
| U-tube with two immiscible liquids | $\rho_1h_1=\rho_2h_2$ (heights above the interface level) |
| Force on a vertical wall (width $b$, depth $H$) | $F=\tfrac12\rho gbH^2$, acting at $H/3$ from the bottom; torque about base $\tfrac16\rho gbH^3$ |
| Container accelerating horizontally ($a$) | surface tilts: $\tan\theta=a/g$ |
| Container accelerating up / down | $P=P_0+\rho(g\pm a)h$; free fall: no pressure difference |
| Rotating about vertical axis | paraboloid: $h=\dfrac{\omega^2r^2}{2g}$ |
| U-tube accelerating horizontally (arms $L$ apart) | level difference $\dfrac{aL}g$ |
| Rotating U-tube (one arm on axis) | $\Delta h=\dfrac{\omega^2L^2}{2g}$ |
Hydraulic lift, brakes: force multiplied, work not ($F_1d_1=F_2d_2$). Floating: $\dfrac{V_{\text{in}}}V=\dfrac{\rho}{\rho_l}$. Apparent weight $W\left(1-\dfrac{\rho_l}\rho\right)$; relative density $=\dfrac{W}{W-W_{\text{in water}}}$.
| Floating case | Result |
|---|---|
| Body between two liquids | $\rho V=\rho_1V_1+\rho_2V_2$ |
| Ice floating melts | water level unchanged (stone inside ice: level falls; wood/air: unchanged) |
| Lift accelerating | fraction immersed unchanged |
| Hollow sphere just floats (radii $r$, $R$) | $\rho\left(R^3-r^3\right)=\rho_lR^3$ |
| Body released at depth $h$ ($\rho<\rho_l$) | $a=g\left(\dfrac{\rho_l}\rho-1\right)$; rises above the surface to $h\left(\dfrac{\rho_l}{\rho}-1\right)$ (no drag) |
| Beaker on a balance, body hung inside | reading increases by the buoyant force |
| Floating block pushed down and released | SHM, $T=2\pi\sqrt{h/g}$ |
3 more sections and 16 formulas in the full chapter
- 2Fluid flow2 formulas · 1 case table · 1 diagram
- 3Viscosity8 formulas
- 4Surface tension6 formulas · 1 case table
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