Air flows from a reservoir in which the pressure is kept at 124 kPa through a convergent–divergent nozzle and exhausts to the atmosphere where the pressure is 101.3 kPa. Under these conditions, the nozzle is choked and the flow is subsonic on both sides of the throat. To what value must the pressure in the reservoir be increased so that there is a normal shock on the nozzle exit plane?

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j