Total work done in pumping a layer water through a bottleneck

[JustSomeGuy80]

I don't know much about physics but I know that Work = Force x Distance. Does it take more force to pump an x amount of water through a bottleneck (a shrinking radius from a to b and the constant radius from b to c) as opposed to pumping that same amount of water through a constant radius? If so, how do I factor that into the equation?

 

[Gear300]

If the final height of the water is the same, then the same amount of work against gravity should have been done...ideal flow, or laminar flow, disregards collisions against the bottle walls.

 

[astrokreng]

I can explain that the total work done in pumping a layer of water through a bottleneck is determined by both the force applied and the distance over which the force is applied. This can be represented by the equation Work = Force x Distance.

In this situation, pumping water through a bottleneck involves exerting a force to overcome the resistance of the bottleneck and pushing the water through the narrow space. As the radius of the bottleneck decreases from point a to point b, the force required to push the same amount of water through will increase. This is because the bottleneck creates more resistance and therefore requires more force to be applied.

To factor this into the equation, you can consider using the concept of pressure, which is defined as force per unit area. As the radius decreases, the area through which the force is applied decreases, resulting in an increase in pressure. This can be represented by the equation Pressure = Force / Area. Therefore, the total force required to pump the water through the bottleneck can be calculated by multiplying the pressure by the area.

In conclusion, it does require more force to pump the same amount of water through a bottleneck compared to a constant radius, and this can be factored into the equation by considering the concept of pressure.