Fluids travel fastest through which type of needle?

• A. Shorter and larger diameter
• B. Longer and smaller diameter
• C. Shorter and smaller diameter
• D. Longer and larger diameter

Answer: (A)

Flow through a needle follows Hagen-Poiseuille’s principle: the flow rate is proportional to the radius to the fourth power and inversely proportional to the length (Q ∝ r^4 / L) for a given pressure drop and viscosity. This means even small increases in radius dramatically boost flow, while longer length reduces flow more modestly but still decreases it. To maximize how fast fluid travels, you want the largest inner diameter and the shortest length. Among the options, a needle that is shorter and has a larger diameter provides the least resistance and the greatest flow. Shorter with smaller diameter slows flow sharply due to the r^4 term, and longer needles add resistance even if the diameter is large, so they don’t beat the short, wide option.