Conceptual question: Bernoulli's Principle Syringes

[bismuthman]

Homework Statement

I'm interested in an explanation of the forces/principles involved in the following scenario: There are two syringes, level with one another, containing the same volume of water. The difference between the syringes is the gauge of the needle; one is of greater diameter than the other. One wishes to empty both syringes in the same amount of time.

Homework Equations

To empty the syringes in equal time, will one plunger require a greater force than the other?
How will the magnitude of the pressure on the walls of the two syringes vary?
How will the speed of the fluid exiting the syringe compare?
(Sort of vague) What can we learn by applying Bernoulli's principle to the problem?

Lastly:

Thanks you guys. I'm not very physics-minded and have been studying for the MCAT lately. I feel I should be able to understand any scenario in terms of the underlying principles. Not too realistic, but I'm especially interested in this one!

The Attempt at a Solution

 

[Chestermiller]

Hi Bismuthman. Welcome to Physics Forums.

This is not a problem that one would solve using Bernoulli. Because of the tiny diameter of the needle, the fluid flow in this system will be dominated by viscous pressure losses. The intertial pressure variations associated with Bernoulli will be negligible. Have you learned about viscous flow yet? If so, have you studied laminar viscous flow in a tube?

Chet

 

[bismuthman]

My understanding of viscosity is about as thick as a flashcard: the internal friction of a fluid, the resistance of the fluid to motion. I am aware of the distinction between laminar and turbulent flow. What exactly do you mean by laminar viscous flow? Am I to understand that the viscosity of the fluid increases in the needle of either syringe (moreso in the smaller of the two)?

 

[bismuthman]

Edit: Thanks for you answer!

 

[rezeew]

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. In this scenario, the fluid has a constant volume and is being forced out of the syringes at the same rate. However, the syringe with the larger diameter needle will allow for a greater volume of fluid to pass through it in the same amount of time compared to the syringe with the smaller diameter needle.

This means that the fluid in the larger syringe will be moving at a faster speed as it exits the needle, resulting in a lower pressure within the syringe compared to the smaller syringe. This can be explained by Bernoulli's principle, as the faster moving fluid has a lower pressure.

Therefore, to empty both syringes in the same amount of time, the plunger of the larger syringe will require a greater force to push the same volume of fluid through the larger needle. This is because the larger needle offers less resistance to the fluid flow, requiring a stronger force to push it through at the same rate as the smaller needle.

Applying Bernoulli's principle to this problem allows us to understand the relationship between fluid speed and pressure, and how this affects the flow of fluid through different sized openings. In this scenario, we can see how the diameter of the needle can impact the speed and pressure of the fluid, and how this relates to the force required to empty the syringes in equal time. This concept can also be applied to other fluid dynamics problems and is important in understanding the behavior of fluids in various systems.