To double the flow rate in a spray system, how must the pressure change?

To double the flow rate in a spray system, how must the pressure change?

• A. Increase four times
• B. Increase two times
• C. Increase by 50 percent
• D. Decrease

Answer: (A)

Flow rate through a spray nozzle is tied to the pressure drop across the nozzle through a square-root relationship: the exit velocity is proportional to the square root of the pressure difference, and the flow rate is that velocity times the constant nozzle area. Therefore, to double the flow, the pressure difference must increase by a factor of four, because sqrt(4) equals 2. If you only double the pressure, the flow grows by about 1.41 times; a 50% rise in pressure yields roughly a 1.22-fold increase. Decreasing pressure would reduce flow. This fourfold pressure increase is what makes the flow rate doubling in this system, assuming the nozzle and fluid conditions stay the same.

Flow rate through a spray nozzle is tied to the pressure drop across the nozzle through a square-root relationship: the exit velocity is proportional to the square root of the pressure difference, and the flow rate is that velocity times the constant nozzle area. Therefore, to double the flow, the pressure difference must increase by a factor of four, because sqrt(4) equals 2. If you only double the pressure, the flow grows by about 1.41 times; a 50% rise in pressure yields roughly a 1.22-fold increase. Decreasing pressure would reduce flow. This fourfold pressure increase is what makes the flow rate doubling in this system, assuming the nozzle and fluid conditions stay the same.