The power P delivered by a windmill whose blades sweep in a circle of diameter D by a wind of speed v is proportional to the square of the diameter and the cube of the wind speed. Show that this dependence on diameter and wind speed exist when 100% energy transfer takes place. Also show that
`P=pi/8 rhoD^(2)v^(3)`
Where is `rho` the density of air.

The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through in time t? (b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind's energy into electrical energy, and that A=30m^2 , v=36kmh^-1 and the density of air is 1.2kgm^-3 , what is the electrical power produced?

The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity upsilon perpendicular to the circle, what is the mass of air passing through it in time t? (b) What is K.E. of the air ? (c) Assume that the wind mill converts 25% of the wind's energy into electrical energy , and that A=30m^(2), upsilon=36km//h and the density of air is 1.2kg//m^(3) . What is electrical power produced ?

The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter D_(0) and is connected toa large tank of water. The surface of the water is at a height b above the end of the tap. By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given rho_(w) = density of water) The equation for the water speed v as a funcation of the distance x below the tap will be:

The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter D_(0) and is connected toa large tank of water. The surface of the water is at a height b above the end of the tap. By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given rho_(w) = density of water) Equation for the flow rate, i.e. the mass of water flowing through a given point in the stream per unit time, as funcation of the water speed v will be

The human ciculatory system can be thought of as a closed system of interconnecting pipes through which fluid is continuously circulated by two pumps the two pumps the right and left verticles of the heart, work as simple two-stroke force pumps. The muscles of the heart regulate the force by contracting and relaxing. the contraction (systole) lasts about 0.2s and a complete systole/diastole (contraction/relaxation) cycle lasts about 0.8s. For flood pressures and speeds in the normal range. the volume flow rate of blood through a blood vessel is directly proportional tot he pressure difference over a length of the vessel and to the fourth power of the radius of the vessel. The total mechanical energy per unit volume of blood just as it leaves the heart is E//V=rhogh+P+rhov^(2) Q. Which of the following is a way to achieve approximately a 45% increase in the volume flow rate of blood through a blood vessel?

An aircraft is moving on a runway for its take off. The wind speed on the lower and upper surface of the wings are 'v' and 'sqrt2'v . If the density of air is rho and surface area of the wing is A, the upward force exerted on thei wings will be