Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A, B$ and $C$ are shown. Sections $B$ and $C$ have equal area of cross section. If $P_A, P_B$ and $P_C$ are the pressures at $A, B$ and $C$ respectively then
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(b)

Solution by using Bernoulli's principle and equation of continuity Comparing points $A$ and $B$

$A_A V_A=A_B V_B$   {equation of continuity} 

$\because A_A < A_B$

$v_A > v_B$

$P_A+\frac{1}{2} \rho V_A^2+\rho g h=P_B+\frac{1}{2} \rho V_B^2+\rho g h$ {Bernoulli's equation}

$\because v_A > v_B$

$\Rightarrow \frac{1}{2} \rho V_A^2 > \frac{1}{2} \rho V_B^2$

$\therefore P_A < P_B \quad \ldots (1)$

Now comparing $C$ and $B$

$A_B=A_C \Rightarrow v_B=v_C$

[equation of continuity].

$P_B+\frac{1}{2} \rho V^2+\rho g h_B=P_C+\frac{1}{2} \rho V^2+\rho g h_C$

$\Rightarrow P_B+\rho g h_B=P_C+\rho g h_C$

$\because h_B > h_C \text { then } \quad \ldots (2)$

$P_B < P_C$

Using $(1)$ and $(2)$

We can say,  $P_A  <  P_B  <  P_C$

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