In which direction does the Tigris river flow?

What are the factors governing the drag force on a pebble at a river bed?

• From this seemingly harmless question of dimensional analysis: I was reminded having studied about D'Alembert's paradox in my fluid mechanics course. Now in this question since viscosity isn't a relevant parameter, and the density is given, let's start with the simplest case of inviscid, incompressible flow. D'Alembert's paradox has it that such a flow past a ball causes zero drag. So my questions are: 1. Will it hold true in a uniform force field perpendicular to the flow (no drag in in the direction of flow)? 2. Does the result change when we assume the pebble to be placed on the river bed (flat, frictionless for simplicity), given the fact that the flow above and below the object is not same? 3. What happens in the different regimes of high/low viscosity high/low Reynold's number? I would welcome both intuitive as well as mathematical arguments. Please take simple assumptions that help but please state them in your answer.

• Answer:

  Hi !! You have a keen eye...Ofcourse, even in the water....you have to assume a 1-D flow to apply D'alembert's paradox.....the flow MUST be completely symmetric both below and above the pebble which rules out turbulence. So, we are left with Low Re. Having said this, would you mind explaining why m was proportional to v^5 as ticked in your pic above...My slow brain has problems understanding it