QUESTION $10$

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A pitot$-$static tube is placed at the exit plane of a $2-$inch nozzle to measure the total and static pressure of the air jet issuing into ambient atmosphere. From the measurements, the velocity of the air jet at the nozzle exit plane is calculated to be $103\frac{m}{s}.$ Based on this velocity, the engineers estimated that the pitot$-$static probe would experience a force upwards of $25$ lbs $.$ They designed a strain gage based force balance to measure the force experienced by the pitot$-$static probe. The force experienced by the probe is the sum of the forces due to the exit momentum of the jet as well as the jet exit pressure. Calculate the uncertainty in the force measurement $($in N $)$ if the uncertainty in velocity measurement is $+-1\mathrm{.}3\frac{m}{s}$; uncertainty in nozzle exit area measurement is $+-0\mathrm{.}017\%$ and uncertainty in pressure measurement is $+-0\mathrm{.}01.$ Assume density of air to be $1\mathrm{.}225k\frac{g}{m}3.$

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