CDF POINTS
Pressure
It is defined as the force acting normal to a unit surface area. Pressure is a scalar quantity.
\(
P_{avg} = \frac{F}
{A},P = \mathop {\lim }\limits_{\Delta A \to 0} \frac{{\Delta F}}
{{\Delta A}}
\)
SI unit: Nm-2= pascal, CGS unit: dyne/cm2
1Nm-2= -10dyne/cm2,
D.F: \(
ML^{ - 1} T^{ - 2}
\)
Atmospheric pressure can be determined using 'Fortin's Barometer
1atmosphere = 1.013 × 105Pa = 1.013bar
Density
The density of a body is defined as the ratio of mass of the body to the volume occupied by the body
density= \(
\frac{{mass}}
{{volume}}
\) \(
\Rightarrow \rho = \frac{M}
{V}
\)
SI units :\(
kgm^{ - 3}
\),CGS units :\(
gcm^{ - 3}
\)
\(
1g/cc = 10^3 Kg/m^3
\) ;
Dimensional formula= ML-3
Density is a scalar quantity.
Density of a mixture
When two liquids of masses m1,m2 and densities \(\rho_1\), \(\rho_2\) respectively are mixed then the effective density of the mixture is
\(
\begin{gathered}
\Rightarrow \rho = \frac{{M_{total} }}
{{V_{total} }} = \frac{{m_1 + m_2 }}
{{V_1 + V_2 }} \hfill \\
= \frac{{m_1 + m_2 }}
{{\left( {\frac{{m_1 }}
{{\rho _1 }} + \frac{{m_2 }}
{{\rho _2 }}} \right)}} = \frac{{\left( {m_1 + m_2 } \right)\rho _1 \rho _2 }}
{{m_1 \rho _1 + m_2 \rho _2 }} \hfill \\
\end{gathered}
\)
Pascals law
If an external pressure is applied to an enclosed fluid it is transmitted undiminished to every point of the fluid and to the walls of the container.
Applications of Pascals law are, hydraulic lift, hydraulic brakes......
\(
\frac{{F_1 }}
{{A_1 }} = \frac{{F_2 }}
{{A_2 }}
\)
Variation of density with pressure:
With increase in pressure, volume decreases and density increases
\(
\rho _0 = \rho \left[ {1 - \frac{{\Delta P}}
{K}} \right] \Rightarrow \rho = \rho _0 \left[ {1 - \frac{{\Delta P}}
{K}} \right]^{ - 1} \approx \rho _0 \left[ {1 + \frac{{\Delta P}}
{K}} \right]
\)
Where \(\rho_0\)=density at NTP ; p = density at desired pressure;
\(\Delta P\)= increase in pressure,K-Bulk Modulus
Archimede’s Priciple
When a body is immersed partly or wholly in If a fluid it loses some weight, which is equal to in the weight of the fluid displaced by the body