(Solved): 2. An instrument used to measure the airspeed on many early airplanes (about 1919 to 1930) was a Ve ...

2. An instrument used to measure the airspeed on many early airplanes (about 1919 to 1930) was a Venturi tube shown below. Imagine you want to use a Venturi tube with an inlet to throat area ratio of \( 1.4: 1 \) for an airplane with a maximum cruising velocity of \( 60 \mathrm{~m} / \mathrm{s} \). Inside the cockpit is an airspeed indicator - a dial that is connected to a pressure gauge sensing the Venturi tube pressure difference \( p_{1}-p_{2} \) and properly calibrated in terms of velocity. What is the general relationship between this pressure difference and the airplane velocity and what is the maximum pressure difference the pressure gauge has to be able to sense? 3. Consider an airplane flying with a velocity of \( 80 \mathrm{~m} / \mathrm{s} \) at an altitude of \( 3 \mathrm{~km} \). At a point on the wing, the airflow velocity is \( 90 \mathrm{~m} / \mathrm{s} \). Calculate the pressure and temperature at this point. Now the airplane speeds up to a velocity of \( 140 \mathrm{~m} / \mathrm{s} \) and the same point on the wing has an airflow velocity of \( 160 \mathrm{~m} / \mathrm{s} \). What is the pressure and temperature at this point now?