Q10CQ - College Physics (Urone)

Question

Is there a limit to the height to which an entrainment device can raise a fluid? Explain your answer.

Answer

Step-by-Step Solution

Answer

Yes, It’s due to gravity and limitations of the entrainment device.

Step 1: Entrainment

The fluid with higher velocity forces other fluid into the stream when pressure is higher outside.

Step 2: Relation between height, velocity and pressure

Bernoulli’s equation is \(P + 1/2\rho {v^2} + \rho gh = constant\). Here, P is the pressure of the fluid, v is the fluid velocity, h is the height, and ρ is the density of the fluid. From Bernoulli's equation, we can say \({\rm{h}} \propto {{\rm{v}}^{\rm{2}}}\) and \(h \propto P\).

Step 3: Is there a limit to the height.

Yes, there is a limit.

Step 4: Explanation

In an entrainment device, fluid is passed through the smaller cross-sectional area so that the kinetic energy of the fluid is increased. The velocity of fluid inside the entrainment device is dependent on the device i.e., its cross-sectional area and initial pressure of the fluid. There is a limitation on the velocity and hence on the height to which the entrainment device can raise the fluid. Furthermore, gravity acts on the fluid and reduces its velocity. A decrease in velocity will increase the pressure and spreading. Hence, after reaching a certain height, fluid will start to spread and fall.