Fluid Dynamics: Dimensional Analysis and important forces

[K41]

I am stuck on the questions, 5.3.10 and 5.3.11 which are part of a chapter on dimensional analysis in fluid mechanics by Streeter.

Question 5.3.10 (see also the attachment):
It asks me for the given fluid dynamic problems, where is the inertial force not important. It lists several fluid dynamics situations including spillway crest, open channel transition, waves against a sea wall, capillary tube and flow through a half opened valve.

Solution?
I generally understand the inertial force as the resultant force acting on a specific mass, due to applied forces such as pressure, gravity and viscosity. So I don't really understand how the resultant force can ever be "unimportant". The book also mentions that the Froude number is important for free surface flows, but this is not clear to me. I don't understand why is gravity important for free surface flows?

Question 5.3.11 (see also the attachment):
A similar question, asking me to identify which forces are important for laminar flow between closely spaced parallel plates. The forces are inertial, viscous, pressure and gravity.

Solution?
For this I suspect viscous force are important, because of the small, but very large gradients which may be created due to a boundary layer on the edge of each plate, not sure what else though?

There aren't any solutions provided for these questions.

 

[Chestermiller]

I am stuck on the questions, 5.3.10 and 5.3.11 which are part of a chapter on dimensional analysis in fluid mechanics by Streeter.

Question 5.3.10 (see also the attachment):
It asks me for the given fluid dynamic problems, where is the inertial force not important. It lists several fluid dynamics situations including spillway crest, open channel transition, waves against a sea wall, capillary tube and flow through a half opened valve.

Solution?
I generally understand the inertial force as the resultant force acting on a specific mass, due to applied forces such as pressure, gravity and viscosity. So I don't really understand how the resultant force can ever be "unimportant". The book also mentions that the Froude number is important for free surface flows, but this is not clear to me. I don't understand why is gravity important for free surface flows?

Question 5.3.11 (see also the attachment):
A similar question, asking me to identify which forces are important for laminar flow between closely spaced parallel plates. The forces are inertial, viscous, pressure and gravity.

Solution?
For this I suspect viscous force are important, because of the small, but very large gradients which may be created due to a boundary layer on the edge of each plate, not sure what else though?

There aren't any solutions provided for these questions.

The inertial force is what we usually refer to as that associated with mass times acceleration. So, in cases where the mass times acceleration is zero (or very small compared to other forces in the system, so that the other forces are virtually in equilibrium), we say that the inertial forces are negligible. For example, if you have steady flow of a very viscous fluid in a tube, the pressure forces are balanced by the viscous forces, and the inertial forces are zero. Another example is hydrostatic equilibrium of a fluid in a vertical tube, where we have a balance of pressure forces and gravitational forces.

 

[K41]

The inertial force is what we usually refer to as that associated with mass times acceleration. So, in cases where the mass times acceleration is zero (or very small compared to other forces in the system, so that the other forces are virtually in equilibrium), we say that the inertial forces are negligible. For example, if you have steady flow of a very viscous fluid in a tube, the pressure forces are balanced by the viscous forces, and the inertial forces are zero. Another example is hydrostatic equilibrium of a fluid in a vertical tube, where we have a balance of pressure forces and gravitational forces.

Thanks, I still don't see how one can decide where it is in near equilibrium though. Why in a capillary tube for instance, are pressure forces important? Where do they come from in that case?

 

[Chestermiller]

Thanks, I still don't see how one can decide where it is in near equilibrium though. Why in a capillary tube for instance, are pressure forces important? Where do they come from in that case?

Hydrostatic, assuming there is a free surface involved.

 

[K41]

Hydrostatic, assuming there is a free surface involved.

Ah yes, I guess so. I think I was thinking about a syringe so I was thinking the hydrostatic forces would be so small (since syringes are very small). Why does the hydrostatic force need a free surface however?

 

[Chestermiller]

Ah yes, I guess so. I think I was thinking about a syringe so I was thinking the hydrostatic forces would be so small (since syringes are very small). Why does the hydrostatic force need a free surface however?

If you are thinking a syringe, then you have a balance between pressure and viscous forces.