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Pressure Variation

**p**where P1 is pressure at point A and

_{2}= p_{1}+ pgh**P**

_{2}is pressure at point B.

Pascal’s law if the pressure at a point is changed, the change is transmitted to the entire liquid without being diminished in magnitude.

Hydraulic lift principles (a) Pascals law (b) liquids are incompressible

If

**A**

_{1}and

**A**

_{2}are the area of cross-sections in the U – tube on two sides as shown in the and F is the force applied on the side of cross-section

**A**

_{1}then weight lifted is

**W = F A**

_{2}/ A_{1}Barometer measures atmospheric pressure, forty’s barometer is most commonly used to measure atmospheric pressure. Manometers are used to measure partial pressure.

Archimedes’ principle when a body is weighed in a fluid it loses its weight. The weight lost is equal to the weight of the amount of liquid displaced. This is in accordance with Newton’s laws of motion. The buoyant force or up thrust is responsible to decrease the weight

**Wright in the liquid = V (P – σ)g**

Where V is volume displaced, P is density of the body and

**σ**is density of fluid

Weight lost =

**Vσg**

**Specific gravity or relative density = density of body / density of water**

In CGS system, density of a body = specific gravity (without unit)

If

**m**

_{1}and

**m**

_{2}are masses of densities

**P**

_{1}and

**P**

_{2}then the combined density is

**P = m**

_{1 }+ m_{2}/ m_{1}+ m_{2}/ p_{1}p_{2}= ∑ m_{1}/ ∑m_{1}/ p if m_{1}= m_{2}then P = 2P_{1}P_{2}/P_{1}+ p_{2}

If

**v**is volume of density

_{1}**P**

_{1}and

**V**

_{2}is volume of density

**P**

_{2}then the combined density

**P = P**

_{1}V_{1}+ P_{2}V_{2}/ V_{1}+ V_{2}= ∑P_{i}V_{i}/ ∑V_{i }

Variation of density with rise in temperature

**P = P**

_{0}(1 - γ∆θ)Where

**∆θ**is change in temperature and γ is volumetric coefficient of expansion.

Variation of density with volume/ bulk modulus

**P = p**

_{0}V_{0}/ V = P_{0}( 1 + ∆P / B)Floatation a body will float if the weight of the body mg ≤ up thrust or buoyant force

That is P body ≤ P liquid

If P body < P liquid if floats

If P body = P liquid it just floats

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