## Mechanical Properties of Fluids

# Pressure

- Static pressure is the normal force experienced per unit area of cross section P=F/A ⇒ P=ρgh.
- At the bottom of the liquid pressure is mainly due to the weight of the liquid.
- Pressure exerted by liquid only is called Gauge pressure.
- Absolute pressure is equal to atmospheric pressure and gauge pressure.
- Pressure is isotropic, the pressure exerted by a liquid at a point is same in all directions.
- Absolute pressure is always positive and never equal to zero.
- Gauge pressure may be positive negative or zero.
- Pressure exerted by a liquid varies when it accelerates in horizontal or vertical direction.
- Barometer is an instrument used to measure atmospheric pressure.
- Manometer is an instrument used to measure pressure exerted by gases.
- According to pascals law if an external pressure is applied to an enclosed fluid it is transmitted to every points in the fluid undiminished.
- The energy possessed by a fluid by virtue of its pressure is called the pressure energy.
- When two liquids of equal mass are mixed then the effective density \rho=2\frac{\rho_1\rho_2}{\rho_1+\rho_2}
- When two liquids of equal volume are mixed then the effective density \rho=\frac{\rho_1+\rho_2}2
- When a body is partially or wholly immersed the force exerted in the upward direction called buoyancy.

### Pressure View the Topic in this video From 22:38 To 1:05:46

### View the Topic in this video From 0:35 To 59:13

### Pascal's law View the Topic in this video From 0:30 To 16:13

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1. Density of a substance is defined as the mass per unit volume of the substance.

Density, ρ = \tt \frac{Mass(M)}{Volume(V)}

2. Relative density of a substance is defined as the ratio of its density to the density of water at 4°C.

Relative density = \tt \frac{Density\ of\ a\ substance}{Density\ of\ water\ at\ 4°C}

3. When two liquids of same mass m but of different densities ρ_{1} and ρ_{2} are mixed together, then density of mixture is \tt \rho= \frac{2\rho_{1}\rho_{2}}{\rho_{1}+\rho_{2}}

4. When two liquids of same volume V but of different densities ρ_{1} and ρ_{2} are mixed together, then density of mixture is \tt \rho= \frac{\rho_{1}+\rho_{2}}{2}

5. Density of a liquid varies with pressure \tt \rho=\rho_{0}\left[1+\frac{\Delta p}{K}\right]

6. Pressure is defined as the thrust acting per unit area of the surface in contact with liquid.

\tt P=\frac{Thrust(F)}{Area(A)}=\frac{F}{A}

7. Pressure exerted by a liquid column p = hρg

8. Mean pressure on the walls of a vessel containing liquid upto height h is \tt \left(\frac{h\rho g}{2}\right)

9. The pressure p at depth below the surface of a liquid open is given by Pressure, p = p_{a} + hρg

10. Atmospheric pressure = hdg = 76 × 13.6 × 980 dyne/cm^{2}