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 PA, PB and PC are the pressures at A, B and C. respectively then

Question

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 PA, PB and PC are the pressures at A, B and C. respectively then (A) PA > PB=PC (B) PA < PB < PC (C) PA < PB=PC (D) PA > PB > PC

Tardigrade Admin · Accepted Answer

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

}

∵ A_{A} < A_{B}

v_{A} > v_{B}

P_{A} + \frac{1}{2} ρ V_{A}^{2} + ρ g h = P_{B} + \frac{1}{2} ρ V_{B}^{2} + ρ g h

{

Bernoulli's equation

}

∵ v_{A} > v_{B}

\Rightarrow \frac{1}{2} ρ V_{A}^{2} > \frac{1}{2} ρ V_{B}^{2}

∴ P_{A} < P_{B}

...(1)
Now comparing

C

and

B

A_{B} = A_{C} \Rightarrow v_{B} = v_{C}

[equation of continuity]

P_{B} + \frac{1}{2} ρ V^{2} + ρ g h_{B}

= P_{C} + \frac{1}{2} ρ V^{2} + ρ g h_{C}

\Rightarrow P_{B} + ρ g h_{B} = P_{C} + ρ g h_{C}

∵ h_{B} > h_{C}

then ...(2)

P_{B} < P_{C}

Using (1) and (2)
We can say,

P_{A} < P_{B} < P_{C}

Q. 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

$P_{A} > P_{B} = P_{C}$

$P_{A} < P_{B} < P_{C}$

$P_{A} < P_{B} = P_{C}$

$P_{A} > P_{B} > P_{C}$

Q. 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 PA​,PB​ and PC​ are the pressures at A,B and C. respectively then

PA​>PB​=PC​

PA​<PB​<PC​

PA​<PB​=PC​

PA​>PB​>PC​

Q. 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

$P_{A} > P_{B} = P_{C}$

$P_{A} < P_{B} < P_{C}$

$P_{A} < P_{B} = P_{C}$

$P_{A} > P_{B} > P_{C}$