The radius of the tube has the greatest effect on the flow of liquid through a tube because the flow rate is proportional to the fourth power of the radius, causing substantial changes in flow with radius alterations.
Among the listed factors affecting the flow of liquid through a tube, the radius of the tube has the most significant effect. According to Poiseuille's law, the flow rate (Q) through a tube is directly proportional to the fourth power of the radius (r) of the tube, which means any change in radius will result in a substantial change in flow rate. For instance, if the tube's radius is doubled, the resistance to flow decreases by a factor of 24 or 16, thereby significantly increasing the flow rate, all other factors being stable.
The pressure difference, viscosity of the liquid, and length of the tube also play roles in the flow, with the pressure difference being directly proportional to the flow rate and viscosity and length being inversely proportional to it. However, since the radius of the tube affects the resistance to flow exponentially, it is the most impactful on the flow rate of the liquid.
The conclusion is that while the pressure difference, viscosity, and length of the tube are important factors, the radius of the tube has the most pronounced effect on the flow of liquid through a tube.