Final answer:
The radius of the tube has the greatest effect on the flow of liquid through a tube due to its fourth power relationship in the Hagen-Poiseuille equation. Changes in pressure difference, viscosity, tube length, and temperature all influence the flow rate but to varying degrees. so, option d is the correct answer.
Step-by-step explanation:
The student question pertains to the sensitivity of fluid flow rate through a tube. The flow of liquid through a tube can be analyzed using principles from fluid dynamics. Among the factors listed, the radius of the tube has the greatest effect on flow rate, according to the Hagen-Poiseuille equation. It is important to note that changes in each of these factors can impact the flow rate, but the effect that the tube's radius has is due to it being raised to the fourth power in the equation. Therefore, a small change in the radius results in a significantly larger change in flow rate.
Effect of Factors on Fluid Flow Rate
- Increased pressure difference will increase the flow rate.
- Increased viscosity will decrease the flow rate.
- Increased length of the tube will decrease the flow rate.
- A decrease or increase in radius of the tube will significantly decrease or increase the flow rate, respectively.
- Change in temperature may affect viscosity, hence impacting flow rate.
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