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

[Adriano Roma]

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 height 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.

 

[BvU]

Hello Adriano, benvenuto

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 !

 

[Adriano Roma]

Thank you very much, I managed to solve it. I just didn't understand Bernoulli's equation!
Regards