1. An aortic aneurysm exists as a bulging out of the aorta walls, where the aorta walls are actually more elastic than normal aorta walls, and deform more in response to the blood pressure in the aorta. If the radius of the aorta is typically 1 cm and the blood flow rate is 100 cm³ s^-1, how much would the pressure increase in the aortic aneurysm if the radius of the aneurysm is 3 cm? Assume that the blood vessel is horizontal and ignore the viscous nature of blood.

2. You hold a hose at 45o to the horizontal and at a height of 1 m from the floor. The water reaches a maximum distance of 10 m from where you are standing. Now you place your thumb over the end of the hose to occlude the opening by 80%, which in turn reduces the flow rate by 50%. Even though less fluid emerges the water travels further?

a) How far does the water travel with your thumb over the end of the hose (assuming the height and angle remain the same)?

b) Assume the flow rate (as a percentage of original flow rate) can given by

Q_% = 100[1-(A_%/100)⁵]

where is the percentage by which the opening of the hose is occluded. Notice that if is 0% then is 100%, whereas if is 100% then is 0%. Find the amount by which the hose must be occluded in order for the water to travel twice as far (assuming the height and angle remain the same).

3. Assume the muscle is 37^oC and is separated from the outside air by layers of fat and skin. The layer of fat, at a particular location on the skin, is 2 mm thick and has a conductivity of 0.16 W m^-1 K^-1. Above this is a 1.1 mm dermis layer with a thermal conductivity of 0.53 W m^-1 K^-1. Finally, the outermost epidermal layer is 0.1 mm thick with a thermal conductivity of 0.21 W m^-1 K^-1. How much heat is lost per unit area and unit time if the ambient air temperature is 0^oC?