Question

In: Physics

Givens: Altitude: FL310 (31,000 ft Pressure Altitude) Indicated Airspeed: 250 KIAS Indicated Outside Air Temperature (IOAT)...

Givens:

Altitude: FL310 (31,000 ft Pressure Altitude)

Indicated Airspeed: 250 KIAS

Indicated Outside Air Temperature (IOAT) or Total Temperature: -30 deg C

Figure 2.1 for Atmosphere

Figure 3.1 Position Errors

Figure 3.2 Compressibility Errors

Figure 11.2 or Tt = Ta (1 + .2M2) Temperature Ram Rise

1. Find CAS (Calibrated Airspeed in kts).

2. Find EAS (Equivalent Airspeed in kts).

3. Find Pressure Ratio: .

4. Find Mach.

5. Find Actual Outside Air Temperature (ambient temperature).

6. Find Temperature Ram Rise.

7. Find Density Ratio: .

8. Find TAS, True Airspeed in kts.

9. If you are landing into an airfield in mountainous terrain at a field elevation of 3,000 ft

MSL (Mean Sea Level) and the field outside air temperature is -24 deg C, according to

AC 91-XX Draft Appendix 2, how should you adjust your approach arrival procedures

with a Final Approach Fix (FAF) at 5,000 ft MSL and your Minimum Descent Altitude

(MDA) at 3500 ft MSL?

Solutions

Expert Solution

Using the compressible form of Bernoulli's equation and assuming isentropic conditions, the last two equations for EAS and CAS are derived.

Subsonic Fanno Flow for a Given Entrance Mach Number and Pressure Ratio

This situation pose a simple mathematical problem while the physical situation occurs in cases where a specific flow rate is required with a given pressure ratio (range) (this problem was considered by some to be somewhat complicated). The specific flow rate can be converted to entrance Mach number and this simplifies the problem. Thus, the problem is reduced to find for given entrance Mach, , and given pressure ratio calculate the flow parameters, like the exit Mach number, . The procedure is based on the fact that the entrance star pressure ratio can be calculated using . Thus, using the pressure ratio to calculate the star exit pressure ratio provide the exit Mach number, . An example of such issue is the following example that combines also the ``Naughty professor'' problems.



Solution

The star pressure can be obtained from a table or Potto-GDC as
Fanno Flow Input: M k = 1.4
M fld P/P* P0/P0* ?/?* U/U* T/T*
0.25 8.48341 4.35465 2.40271 3.67423 0.272166 1.18519

And the star pressure ratio can be calculated at the exit as following

And the corresponding exit Mach number for this pressure ratio reads
Fanno Flow Input: Pbar k = 1.4
M fld P/P* P0/P0* ?/?* U/U* T/T*
0.60694 0.464084 1.74184 1.18013 1.55848 0.641652 1.11766

A bit show off the Potto-GDC can carry these calculations in one click as

Fanno Flow Input: M1 P2/P1 k = 1.4
M1 M2 fld P2/P1
0.25 0.606934 8.0193 0.4


While the above example show the most simple form of this question, in reality this question is more complicated. One common problem is situation that the diameter is not given but the flow rate and length and pressure (stagnation or static) with some combination of the temperature. The following example deal with one of such example.

Solution

The direct mathematical solution isn't possible and some kind of iteration procedure or root finding for a representative function. For the first part the ``naughty professor'' procedure cannot be used because is not provided and the other hand is not provided (missing Diameter). One possible solution is to guess the entrance Mach and check whether and the mass flow rate with the ``naughty professor'' procedure are satisfied. For Fanno flow at for several Mach numbers the following is obtained
Fanno Flow Input: M1 P2/P1 k = 1.4
M1 M2 fld P2/P1 Diameter
0.1 0.111085 13.3648 0.9 0.00748
0.15 0.16658 5.82603 0.9 0.01716
0.2 0.222018 3.18872 0.9 0.03136

From the last table the diameter can be calculated for example for as

The same was done for all the other Mach number. Now the area can be calculated and therefor the can be calculated. With this information the ``naughty professor'' is given and the entrance Mach number can be calculated. For example for one can obtain the following:

The same order as the above table it shown in ``naughty professor'' (isentropic table).
Isentropic Flow Input: M k = 1.4
M T/T0 ?/?0 A/A* P/P0 PAR F/F*
1.5781 0.667521 0.364051 1.2329 0.243012 0.299609 0.560088
0.36221 0.974432 0.9373 1.7268 0.913335 1.57714 0.777844
0.10979 0.997595 0.993998 5.30922 0.991608 5.26466 2.23063

The first result are not reasonable and this process can continue until the satisfactory solution is achieved. Here an graphical approximation is shown.

Figure 9.20: Diagram for finding solution when the pressure ratio and entrance properties ( and are given

From this exhibit it can be estimated that . For this Mach number the following can be obtained

Fanno Flow Input: M1 P2/P1 k = 1.4
M1 M2 fld P2/P1
0.18 0.19985 3.98392 0.9

Thus, the diameter can be obtained as

The flow rate is

Isentropic Flow Input: M k = 1.4
M T/T0 ?/?0 A/A* P/P0 PAR F/F*
0.1719 0.994125 0.985377 3.42655 0.979587 3.35661 1.45645

Related Solutions

1. A plant is located at an altitude where the atmospheric pressure head is 31 ft...
1. A plant is located at an altitude where the atmospheric pressure head is 31 ft of water and the vapor pressure is 9.34 psi. The pump is placed 10 ft below the water tank with a total suction pipe length of 25 ft, pipe diameter 3 in., and friction coefficient 0.02. Assuming the given atmospheric pressure in the tank (where z1 = 10 ft and negligible velocity) and if the flowrate provided is 180 gpm, determine the available NPSH...
Describe the composition of the Earth’s atmosphere, including the variation with altitude of the temperature, pressure...
Describe the composition of the Earth’s atmosphere, including the variation with altitude of the temperature, pressure and density.
Air flows through a constant area duct. The pressure and temperature of the air at the...
Air flows through a constant area duct. The pressure and temperature of the air at the inlet to the duct are P1 = 100 kPa absolute, and T1 = 298 K, respectively. Inlet Mach number is M1 = 0.1. Heat is transferred to the air as it flows through the duct and as a result the Mach number at the exit increases. Write a Matlab code and plot the following: a) Find the pressure and temperature at the exit, while...
A thermometer is taken from an inside room to the outside, where the air temperature is...
A thermometer is taken from an inside room to the outside, where the air temperature is −15° C. After 1 minute the thermometer reads 13° C, and after 5 minutes it reads −1° C. What is the initial temperature of the inside room? (Round your answer to two decimal places.) c = ?
An outside-air sample is taken on a day when the temperature is 78 F and the...
An outside-air sample is taken on a day when the temperature is 78 F and the relative humidity is 40%. (a) Use the psychrometric chart to state as many physical properties of the air as you can without doing any calculations. For each one, provide a brief description of the property listed. (b) A thermometer is mounted on the back porch of your house. What temperature would it read for the air described in this problem? (c) A sample of...
using the temperature of air, barometric pressure, and volume of flask, calculate moles of air for...
using the temperature of air, barometric pressure, and volume of flask, calculate moles of air for each trial. trial 1: temperature of air: 20.1 deg Celcius, barometric pressure: 742.44 Hg, volume of flask: 285 ml Trial 2: Temp of air 20.2 deg celcius. Barametric pressure: 742.44 Hg , volume : 285 ml
Consider an ideal Brayton cycle with reheat (air standard). The pressure and temperature of the air...
Consider an ideal Brayton cycle with reheat (air standard). The pressure and temperature of the air at the inlet of the gas turbine is 1200 kPa and 1000 K respectively. Assume the gas expands to 100 kPa in two stages. Between the stages, the air is reheated at a constant pressure of 350 kPa to 1000 K. Assume a fully isentropic process in the turbines. Find: (a) the work produced at each stage, in kJ/kg of air flowing. (b) the...
1.How do air temperature and pressure change with height?
1.How do air temperature and pressure change with height?
The air pressure in a tire sitting outside is 30 psi on a nice fall day...
The air pressure in a tire sitting outside is 30 psi on a nice fall day when the temperature is about 80 F. (Assuming that the density of the air inside the tire does not change with temperature and that the air may be treated as an ideal gas), what would the tire pressure be: A) At 32 F? B) At 100 F? If the recommended tire pressure is between 28 and 32 psi, do you need to do anything...
Air at a pressure of 350 kPa, a temperature of 80°C, and a velocity of 180...
Air at a pressure of 350 kPa, a temperature of 80°C, and a velocity of 180 m/s enters a convergent–divergent nozzle. A normal shock occurs in the nozzle at a location where the Mach number is 2. If the air mass flow rate through the nozzle is 0.7 kg/s, and if the pressure on the nozzle exit plane is 260 kPa, find the nozzle throat area, the nozzle exit area, the temperatures upstream and downstream of the shock wave, and...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT