What is the relationship between flow rate and pressure in a sprayer system?

What is the relationship between flow rate and pressure in a sprayer system?

• A. Flow rate varies directly with pressure
• B. Flow rate varies in proportion to the square root of the pressure
• C. Flow rate is independent of pressure
• D. Flow rate varies with the square of pressure

Answer: (B)

In a sprayer, the flow through a nozzle behaves like flow through an orifice. The discharge rate through a fixed nozzle is proportional to the square root of the pressure driving it. That comes from the orifice flow relation Q = C_d A sqrt(2P/ρ), so as pressure increases, flow rises, but not linearly—doubling pressure increases flow by about 1.414 times, not by a full factor of two. This is why flow rate varies with the square root of pressure rather than directly with pressure or with pressure squared.

In a sprayer, the flow through a nozzle behaves like flow through an orifice. The discharge rate through a fixed nozzle is proportional to the square root of the pressure driving it. That comes from the orifice flow relation Q = C_d A sqrt(2P/ρ), so as pressure increases, flow rises, but not linearly—doubling pressure increases flow by about 1.414 times, not by a full factor of two. This is why flow rate varies with the square root of pressure rather than directly with pressure or with pressure squared.