What is the Optimum Height for Drinking a Milkshake with a Vertical Straw?

In summary, the conversation revolved around the inability to drink a chocolate milkshake through a vertical straw due to the pressure difference between the bottom and top of the straw, which is shorter than the straw itself. To determine the optimum height of the straw above the milkshake, Bernoulli's equation can be used to calculate the pressure difference and ensure it is slightly less than the pressure head corresponding to the difference. The conversation also included a helpful illustration to better visualize the problem.
  • #1
Adriano Roma
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You and a friend of yours went for a drink of chocolate milkshake(ρ=1200 kg/m3). The waiter brings your drink in two glasses 200 mm tall with a straw 8 mm in diameter and 300 mm long. Given that human lungs capacity can develop approximately 3000 Pa of vacuum pressure and assuming that the straw is barely inserted into the milkshake:
(a) Verify that you won't be able to drink the milkshake through the vertical straw.
(b) Determine the optimum height of the vertical straw above the milkshake that allows the drink to just flow to your mouth.

As far as I understood, for point (a) I think I need to verify that the pressure head corresponding to the pressure difference between the bottom and the top of the straw is shorter than the straw and for point (b) I would say that the hight of the straw above the drink has to be slightly less than the pressure head corresponding to the pressure difference.

I think I need to apply Bernoulli's equation but don't know how to proceed!

Could you please give me some hints? I attached an image which illustrates the problem.

Thank you in advance.
 

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  • #2
Hello Adriano, benvenuto :welcome:

Bernoulli's equation is an energy balance. In this case a pressure difference calculation is sufficient. For a, and for b too !

PS nice illustration !
 
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Likes Adriano Roma
  • #3
Thank you very much, I managed to solve it. I just didn't understand Bernoulli's equation!
Regards
 

1. What is Bernoulli's equation and how does it work?

Bernoulli's equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation of a fluid in motion. It states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid remains constant at any point along a streamline.

2. How is Bernoulli's equation applied in real-world situations?

Bernoulli's equation is commonly used in the design and analysis of fluid flow systems, such as in aerodynamics, hydraulics, and ventilation. It can also be applied to calculate airspeed, lift force, and other important parameters in aircraft design and operation.

3. Can Bernoulli's equation be applied to all types of fluids?

No, Bernoulli's equation is only applicable to inviscid, incompressible fluids with steady flow. This means that it cannot be used for fluids with high viscosity or compressibility, or for fluids with unsteady flow patterns.

4. What are some common misconceptions about Bernoulli's equation?

One common misconception is that Bernoulli's equation implies that the speed of a fluid increases as its pressure decreases. However, this is not always the case as the velocity and pressure are influenced by other factors such as the geometry of the system and external forces.

Another misconception is that Bernoulli's equation can only be applied to idealized, simplified situations. In reality, it can be used in a wide range of practical applications with reasonable accuracy.

5. Are there any limitations or weaknesses of Bernoulli's equation?

As mentioned earlier, Bernoulli's equation is only applicable to certain types of fluids and flow conditions. Additionally, it assumes that the fluid is inviscid, which may not be true in all situations. It also does not take into account any external forces acting on the fluid, such as gravity or surface tension, which may affect the accuracy of the results.

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