09matthew said:You have been given a milkshake (ρ = 1200kg/m^3). The glass is 200mm tall a straw 8mm diameter and 300mm long.[/QUOTE
i think one should calculate the pressure difference required for the liquid to rise to the upper point of the straw and the velocity of the liquid may be sufficient only to pour out in the mouth- one can take a unit volume for estimation of the required pull from the lungs.
09matthew said:Show that human lungs would be unable to drink the milkshake through a vertical straw.
09matthew said:and also, is z1 = 200mm (size of the cup) and z2 = 300mm (size of the straw)?
Bernoulli's equation is a mathematical equation that relates the pressure, velocity, and height of a fluid in a steady flow. It states that the total energy of a fluid remains constant throughout the flow.
Bernoulli's equation can be rearranged to solve for pressure by subtracting the kinetic energy and potential energy terms from the total energy term. This results in the equation P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2, where P is pressure, ρ is density, v is velocity, and h is height.
The units of pressure are typically measured in pascals (Pa), the units of velocity are meters per second (m/s), and the units of height are meters (m). Density is typically measured in kilograms per cubic meter (kg/m^3). It is important to ensure that all units are consistent when using Bernoulli's equation to calculate pressure.
Bernoulli's equation can be used to calculate pressure in any fluid that is in a steady flow. However, it is important to note that it assumes the fluid is incompressible, non-viscous, and irrotational. These assumptions may not hold true for all fluids, so caution should be taken when using the equation.
Bernoulli's equation has many practical applications, such as calculating the pressure drop in a pipe system, determining the lift force on an airplane wing, and understanding the flow of blood in the human body. It is also commonly used in the design and analysis of pumps, turbines, and other fluid systems.