You are testing a new jet engine in a test cell at sea level conditions. You measure the mass flow through the engine and find it is 125 kg/sec of air plus 2.5 kg/sec of fuel. The velocity ahead of the engine may be assumed to be zero (it is a static test). The velocity of the exhaust is 340 meters/second. The load cell in the test stand (which measures engine thrust) reads 60,000 Newtons. Is the load cell reading correctly within 2%? If not, what should the load cell read?

The answer is 43350 newton

Explanation:

As per the question,

Mass=125.

Air = 2.5

Velocity=340.

So the formula is,

F=ma.

Total=125+2.5=127.5

Applies the formula now,

F=ma

force = 340*127.5 = 43350

Calculate error now,

Error = ((actual-calculated) / actual))

(43350-60000) / 43350 = - 38.40%

Hence greater than 2%.

43248 newtons.

Explanation:

Force = mass x accelerations and units of force are newtons which are given in the question.

here mass = 125 of air and 2.2 of fuel, total = 125+2.2=127.5kg/s and the velocity of the exhaust is 340m/s.

force = 340m/s * 127.5kg/s = 43248 newtons technically this is wrong (observe units) but i will expalin how i have taken acceleration as a velocity here and mass/unit time as simply mass.

see force is mass times acceleration or deceleration, here our velocity is not changing therefore it is constant 340m/s but if it were to change and become 0 in one second then there would be - 340m/s^2 (note the units) of deceleration and there would be force associated with it and that force is what i have calculated here. similarly there would be mass in flow rate of mass per second, which is also in that one second of time.

let's calculate error.

error = (actual-calculated) / actual. = (43248-60000) / 43248 = - 38.734% less is ofcourse greater than 2%.

So the load cell is not reading correct to within 2% and it should read 43248newtons.