Question

A milkshake has a viscosity of 0.40 Pa ⋅ s. To drink this shake through a straw of diameter 0.56 cm and length 22 cm, you need to reduce the pressure at the top of the straw to less than atmospheric pressure. If you want to drain a 400 ml shake in 3.0 minutes, what pressure difference is needed?

Answer 1

To calculate the pressure difference needed to drink a milkshake through a straw, Poiseuille's law is used, requiring the viscosity of the milkshake, the flow rate of consumption, and the dimensions of the straw.

Step-by-step explanation:

The question involves finding the pressure difference required to drink a milkshake with known viscosity through a straw of specific dimensions within a set amount of time. This problem requires knowledge of fluid dynamics, specifically the Poiseuille's law, which relates the flow rate of a fluid through a pipe with the pressure difference, the viscosity of the fluid, and the dimensions of the pipe.

To begin solving this problem, the flow rate (Q) of the milkshake must be calculated. The flow rate is the volume of milkshake consumed divided by the time it takes to consume it, given in cubic meters per second (m³/s). Using the dimensions of the straw, the viscosity of the milkshake (η), and the flow rate (Q), the pressure difference (ΔP) can then be calculated using the formula derived from Poiseuille's law: ΔP = (8 η L Q) / (π r^4), where L is the length of the straw and r is its radius.