Viscous Friction Eats Away Head Along a Pipe
Water comes out weak at the end of a long pipe because viscous friction has been shaving off pressure the whole way. Drag the flow to watch how the water levels in gauges along the pipe step down.
Stand thin gauges (piezometers) along the pipe and the water height steps down from inlet to outlet. That height is the pressure head at each point. Drag the flow and the more that flows, the steeper the slope, so it drops more by the end. Viscous friction is eating the flow's energy a little at a time along the way.
The longer the pipe, the longer friction has to act, so the loss grows with it. Drag the pipe length L and the head loss rises in direct proportion. A pipe twice as long has twice the loss (all else equal). That is why a water main running farther loses more pressure.
Raise the speed and the loss grows much faster. In turbulent flow the head loss is proportional to the square of the speed. Drag the velocity v and the curve shoots up as a parabola. Double the speed and the loss quadruples. That is why pushing the flow rate too high starves the pressure fast.
All of this gathers into one Darcy–Weisbach equation: hf = f LDv²2g. It is the product of a friction factor f, the length-to-diameter ratio LD, and the velocity head v²2g. Drag the velocity v and the bars for each term and the final hf move together. The smaller the diameter D, the larger LD, so the loss climbs sharply.
The friction factor f depends on how rough the inside of the pipe is. Drag the relative roughness εD: a smooth new pipe has a small f, while a rusty, rough old pipe has a larger f, so the same flow loses more. This is what the Moody chart tells us. That is why old plumbing gives weak water at the end even with the same pump. In the next lesson we leave the pipe and follow the boundary layer that flow builds against a surface.