Notes Reminder: please turn in HW, pick up new one Reminder: First Exam next Friday, 1:55-3:50pm, Jordan Hall lab room – Will cover Gravity, Fluids (Ch.13, 14) – Review Session: Colloquium Today: “Through thick and thin – imaging the microscopic structure of non-Newtonian flow behaviors in colloidal suspensions”
Archimedes’ Principle A body wholly or partially immersed in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid displaced by the body.
A piece of aluminum with mass 1kg and mass density 2700 kg/m 3 is suspended from a string, in air, and is then completely immersed in a container of water. Calculate the tension in the string (a) before and (b) after the metal is immersed. air = g/cm 3.
Fluid Dynamics Moving fluids “Ideal” Fluids have – steady flow (non-turbulent) – Incompressible flow – Non-viscous flow – Irrotational flow
Continuity
The cross-sectional area of a typical aorta is 3cm 2, and the velocity of blood flow there is around 30 cm/s. A typical capillary has a diameter of 6 m and hence a cross-sectional area of 3×10 -7 cm2. Blood flowing in a capillary moves at about 0.05 cm/s. Approximately how many capillaries are there in your body?
Bernoulli’s Equation fluid flow in a volume bounded by streamlines
Bernoulli Demos
siphons
Venturi Meter
Skyscraper design: wind blows past a tall building at 11.2 m/s. Calculate the net force on a window pane of dimensions 4.0×3.0m if the air pressure inside the building is standard atmospheric pressure. Assume the density of gas is constant at 1.3 kg/m 3.
Lift: Flow over Airfoils
The Jet d’Eau in Geneva is a water fountain 140 meters high that has become a landmark of the Geneva waterfront. (a) What is the speed of the water as it exits the nozzle? (b) It’s claimed that there are 7000 liters of water in the air at any time. What is the flow rate? (c) What is the nozzle radius? (d) The pump station is partially submerged, 3 meters below the nozzle. If the nozzle is fed by a 20cm radius pipe from the pump, what is the pressure that the pump must produce?
A large keg of height H and cross-sectional area A 1 is filled with your favorite beverage. The top is open to the atmosphere. There is a spigot with an opening of area A 2 at the bottom of the keg. (a) Find the speed of the beverage exiting the spigot when the liquid inside has reached a height h. (b) Find the rate of change of the level of the beverage dh/dt when it has reached a height h inside the keg. (c) Find h as a function of time, assuming the keg is full at time t = 0. (d) How long does it take for the keg to empty if it drains steadily?
A siphon is set up to move water from one tank to another, as shown. (a) What is the speed of the water in the tube? (b) What is the pressure at the highest part of the tube?