Pressure in Fluids

$\mathrm{P}={\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{R}}$

on expansion $\mathrm{R}$ increase, as a result, $\mathrm{P}$  decreases.

v? ²/2 + P? /ρ + gh? = v? ²/2 + P? /ρ + gh?

⇒ v? ²/2 + (P? + ρgh + mg/A)/ρ + g * 0 = v? ²/2 + P? /ρ + g * 0

⇒ v? ²/2 + (ρgh + mg/A)/ρ = v? ²/2 . (1)

Using Continuity equation, we can write
Av? = av? ⇒ v? = (a/A)v?

Putting the value of v? in equation (1), we have
(a²/A²)v? ²/2 + (ρgh + mg/A)/ρ = v? ²/2 ⇒ (A² - a²)/A² * v? ²/2 = (ρgh + mg/A)/ρ

⇒ v? = √ [ (A²/ (A²-a²) * 2 (ρgh + mg/A)/ρ] = 3.09 m/s ≈ 3 m/s