An ideal liquid is flowing in two pipes, one is inclined and second is horizontal. Both the pipes are connected by two vertical tubes, of length h1 and h2 as shown in the figure. The flow is streamlined in both the pipes. If velocity of liquid at A, B, C are 2 m/s, 4 m/s and 4m/s respectively. the velocity at D will be m/s

Engineering

Physics

BernoulIis Equation and Equation of Continuity

Question

An ideal liquid is flowing in two pipes, one is inclined and second is horizontal. Both the pipes are connected by two vertical tubes, of length h₁ and h₂ as shown in the figure. The flow is streamlined in both the pipes. If velocity of liquid at A, B, C are 2 m/s, 4 m/s and 4m/s respectively. the velocity at D will be $2 \sqrt{N}$ m/s^–1. Fill the value of N in OMR

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$P_{1} + \frac{1}{2} {ρv}_{1}^{2} = P_{2} + \frac{1}{2} {ρv}_{2}^{2}$

$P_{1} - P_{2} = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2}) = \frac{1}{2} ρ (16 - 4) = \frac{1}{2} ρ \times 12 = 6 ρ$

$P_{1} + ρ {gh}_{1} + ρ g (h_{2} - h_{1}) + \frac{1}{2} {ρv}_{3}^{2} = P_{2} + {ρgh}_{2} + \frac{1}{2} {ρv}_{4}^{2}$

$6 ρ + \frac{1}{2} {ρv}_{3}^{2} = \frac{1}{2} {ρv}_{4}^{2}$