Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation P₁ – P₂ = ρg (h₂ – h₁)

Statement II : In ventury tube shown $2gh={\nu }_1^2-{\nu }_2^2$

In the light of the above statements, choose the most appropriate answer from the options given below.
 

Concept:

Bernoulli's equation - 

The equation states that the total mechanical energy along a streamline is constant.

$P_1+\rho g{h}_1+\frac{1}{2}\rho v_1^2=P_2+\rho g{h}_2+\frac{1}{2}\rho v_2^2$

Where, P = The pressure exerted by the fluid at a given point in the flow.

$\frac{1}{2}\rho v^2$ This represents the kinetic energy per unit volume of the fluid due to its motion.

Calculation:

Applying Bernoulli's equation

$P_1+\rho g{h}_1+\frac{1}{2}\rho v_1^2=P_2+\rho g{h}_2+\frac{1}{2}\rho v_2^2$

[h₁ & h₂ are are height of point from any reference level]

Given V₁ = V₂ = 0 (for statement-1)

∴ P₁ - P₂ = ρg (h₂ - h₂)

For statement-2

$P_1+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$

P₁ - P₂ = ρgh

$P_1-P_2=\frac{1}{2}\rho v_2^2-\frac{1}{2}\rho v_1^2$

$\rho gh=\frac{1}{2}\rho v_2^2-\frac{1}{2}\rho v_1^2$

$2gh=v_2^2-v_1^2$

∴ The correct option is (4)