Final answer:
To drain a 400 ml shake in 3.0 minutes, you can use Bernoulli's equation to calculate the pressure difference needed. Unfortunately, the given information does not include the density of the shake, so an exact answer cannot be provided without that information.
Step-by-step explanation:
To drain a 400 ml shake in 3.0 minutes, we can use Bernoulli's equation to calculate the pressure difference needed. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume is constant along a streamline. In this case, since the shake is being drained, the kinetic energy and potential energy can be ignored.
Using Bernoulli's equation, we have P1 + 0.5ρv1^2 + ρgh1 = P2 + 0.5ρv2^2 + ρgh2, where P1 and P2 are the pressures at the two points, v1 and v2 are the velocities at the two points, ρ is the density of the shake, g is the acceleration due to gravity, and h1 and h2 are the heights at the two points.
Since the shake is being drained, the pressure at the second point (P2) is atmospheric pressure, which is 1 atm. The height at the two points can be ignored since the shake is being drained in a horizontal pipe. Substituting the given values, we have P1 + 0.5ρv1^2 = 1 atm. Rearranging the equation, we can solve for the pressure difference needed, which is P1 - 1 atm.
It's important to note that the density (ρ) of the shake is needed to accurately solve the equation. Unfortunately, the given information does not include the density of the shake, so we are unable to provide an exact answer without that information.