physics-class-11-unit-10-chapter-03-mechanical-properties-of-fluids-3-lecture-3-5-zd921d49wkq

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Pascal's Principle </primary>
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- The pressure applied to a confined fluid increase the pressure throughout by the same amount.

- <span style="color:green">Applications</span>

- Hydraulic brakes

- Hydraulic lifts

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<footer style = "font-size: 18px">Mechanical Properties of Fluids $\rightarrow$ Pascal's Principle $\rightarrow$ <span style = "color:blue"> Pascal's Principle </span> $\rightarrow$ Pascal's Principle in Hydraulic Lifts $\rightarrow$ Pascal's Principle </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Pascal's Principle in Hydraulic Lifts </primary>
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- $ P_{in}$ = $ P_{out} $

- $\frac {F_{in}}{A_{in}} =\frac {F_{out}}{A_{out}}$

- $F_{out} =F_{in}\frac{A_{out}}{A_{in}}$

- $\frac{A_{out}}{A_{in}}$ is called as the <span style="color:blue">mechanical advantage</span>.

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<footer style = "font-size: 18px">Pascal's Principle $\rightarrow$ Pascal's Principle $\rightarrow$ <span style = "color:blue"> Pascal's Principle in Hydraulic Lifts </span> $\rightarrow$ Pascal's Principle $\rightarrow$ Pascal's Principle </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Pascal's Principle </primary>
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- $P_1$ pressure on the top surface (downwards)

- $P_2$ pressure on the bottom surface (upwards)

- $A$ Area of cross section

- $h_1$ height of the top measure from the surface

- $h_2$ height of the bottom measure from the surface

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<footer style = "font-size: 18px">Pascal's Principle $\rightarrow$ Pascal's Principle in Hydraulic Lifts $\rightarrow$ <span style = "color:blue"> Pascal's Principle </span> $\rightarrow$ Pascal's Principle $\rightarrow$ Buoyancy and Archimedes Principle </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Pascal's Principle </primary>
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- $P_1 = \rho {gh_1}$

- $F_1=P_1 A=\rho{gh_1} A $

- $ P=\rho{gh_2} $

- $ F_2=p g h_2 A $

- $f_{net}=F_2-F_1=\rho g(h_2-h_1) A $

- $=\rho g h A $

- $=\rho g V=m g$

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<footer style = "font-size: 18px">Pascal's Principle in Hydraulic Lifts $\rightarrow$ Pascal's Principle $\rightarrow$ <span style = "color:blue"> Pascal's Principle </span> $\rightarrow$ Buoyancy and Archimedes Principle $\rightarrow$ Buoyancy and Archimedes Principle </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Buoyancy and Archimedes Principle </primary>
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- **Archimedes (287-212 BC)**

- The buoyant force on the cylinder is equal to the weight of the liquid  displacement by the cylinder.

- $W_A>F_B$

- $F_{net}=F_2-F_1$

- $=F_B$
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<footer style = "font-size: 18px">Pascal's Principle $\rightarrow$ Pascal's Principle $\rightarrow$ <span style = "color:blue"> Buoyancy and Archimedes Principle </span> $\rightarrow$ Buoyancy and Archimedes Principle $\rightarrow$ Problem </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Problem </primary>
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- A $10 {kg}$ solid object has an apparent Weight of $8.4 {kg}$ when submerged in a fluid of dencity $3.2 \times 10^3 {kg} / {m}^3$ what is the dencity of  the solid object ?

- **Solution**

- $W_{apparent} = W_{actual}$

- $W_B = \rho_s g V-\rho g V$

- $\frac{W_{actual}}{W_{actual}-W_{apparent}} = \frac{\rho_s g V}{\rho g V}$

- $=\frac{\rho_{s}}{\rho} = \frac {10 {kg}}{10{kg}-8.4{kg}}$

- $\rho_s = \frac{10}{1.6}\times{3.2}\times{10}^3 {kg/m^3}$ = $20\times10^3 {kg/m^3}$

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<footer style = "font-size: 18px">Buoyancy and Archimedes Principle $\rightarrow$ Buoyancy and Archimedes Principle $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Streamline Flow and Continuity Equation $\rightarrow$ Streamline Flow and Continuity Equation </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Streamline Flow and Continuity Equation </primary>
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- $v_P, v_Q, v_R \rightarrow$ velocities.

- $A_P, A_Q, A_R  \rightarrow$ stress of cross section.

- $\rho_P, \rho_Q, \rho_R \rightarrow$ densities.

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<footer style = "font-size: 18px">Buoyancy and Archimedes Principle $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Streamline Flow and Continuity Equation </span> $\rightarrow$ Streamline Flow and Continuity Equation $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Mechanical Properties Of Fluids 3 L-3 </Success>
### <primary style="font-size:24px"> Streamline Flow and Continuity Equation </primary>
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- Mass of liquid flowing is constant.

- $\rho_p A_P v_P \Delta t =\rho _Q A_Q v_Q \Delta t = \rho_R A_R v_R \Delta t$

- $A_Pv_P = A_B v_Q = A_R v_R$

- $Av$ =constant $\rightarrow$ Streamline flow

- $Av$ : flux or the flow rate.

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<footer style = "font-size: 18px">Problem $\rightarrow$ Streamline Flow and Continuity Equation $\rightarrow$ <span style = "color:blue"> Streamline Flow and Continuity Equation </span> $\rightarrow$ Thank You $\rightarrow$  </footer>