If the density of air is ρa and that of the liquid ρl, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

Pressure at point in nozzle → PP=P0 + 1/2ρaV₁².. (1)
P=P0 + 1/2ρlV₂² - ρlgh.. (2)
Equation (1) and (2)
1/2ρaV₁²=1/2ρlV₂² + ρlgh
Neglecting the terms
ρgh
V₂² = √(ρaρl)V₁²
Rate of liquid flow=AV₂=AV₁√(ρaρl)
Rate of liquid flow ∝ √(ρaρl)