To double the flow rate of a system, by how much must the pressure be increased?

• A. Fivefold
• B. Fourfold
• C. Threefold
• D. Twofold

Answer: (B)

To double the flow rate of a system, the pressure must be increased fourfold. This relationship is established by applying the principles of fluid dynamics, particularly the Bernoulli's equation and the Hagen-Poiseuille equation, which describe how pressure, flow rate, and resistance are interrelated in a fluid system.

Flow rate is proportional to the pressure differential driving the fluid through a system, meaning that if the flow rate is to be doubled, the increase in pressure needs to account for the resistance or frictional losses as well. Specifically, for laminar flow through a cylindrical pipe, the flow rate is directly proportional to the fourth power of the radius of the pipe and directly proportional to the pressure difference, while inversely proportional to the viscosity and length of the pipe.

Thus, when dealing with ideal conditions and consistent system characteristics, doubling the flow rate implies requiring four times the pressure because of the squared relationship between flow rate and pressure in many systems. Therefore, the pressure must increase fourfold to achieve the desired effect on flow rate.