Question

A liquid flows in the tube from left to right as shown in figure.A1 and A2 are the cross section of the portions of the tube as shown.the ratio of speed ,v1÷v2 will be

Answer 1

ratio of v₁ and v₂ is A₂ : A₁

here we should apply equation of continuity

equation of continuity states that the rate at which mass enters the system is equal to the rate at which mass leaves the system.

⇒ρ₁A₁v₁ = ρ₂A₂v₂

here ρ is density of fluid, A is cross sectional area and v is velocity of flow of fluid.

if fluid is same

then, A₁v₁ = A₂v₂

⇒v₁/v₂ = A₂/A₁

hence ratio of v₁ and v₂ is A₂ : A₁

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Answer 2

The ratio of speed v₁ ÷ v₂ will be A₂ ÷ A₁

Explanation:

The figure given in the question is attached below.

The flow in the inlet is given as:

Δv/Δt = (A₁v₁Δt)/Δt

∴ Δv/Δt = A₁v₁

The flow in the inlet is given as:

Δv/Δt = (A₂v₂Δt)/Δt

∴ Δv/Δt = A₂v₂

The equation of continuity is given as:

A₁v₁ = A₂v₂

Now, the ratio of the velocity is given as:

∴ v₁/v₂ = A₂/A₁