Holooly Plus Logo
Holooly Plus Logo

Question 17.SP.44: A jet plane travels through the air with a speed of 1000 km/......

A jet plane travels through the air with a speed of 1000 km/h at an altitude of 6 km, where the pressure is 40 kPa and the temperature is −12°C. Consider the inlet diffuser of the engine where air leaves with a velocity of 100 m/s. Determine the pressure and temperature leaving the diffuser, and the ratio of inlet to exit area of the diffuser, assuming the flow to be reversible and adiabatic.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

V = 1000 km/h = 277.8 m/s,  v _1=\frac{ RT }{ P }=\frac{0.287 \times 261.15}{40}=1.874 \,m ^3 / kg

\begin{aligned}& h _1=261.48 \,kJ / kg , P _{ r 1}=0.6862 \\& h _{ o 1}=261.48+277.8^2 / 2000=300.07 \,kJ / kg \\& \Rightarrow T _{ o 1}=299.7 \,K , \quad P _{ ro1 }=1.1107\end{aligned}

The ratio of the pressures equals the ratio of the Pr functions when s = constant

\begin{aligned}& P _{ o 1}= P  P _{ ro1 } / P _{ r 1}=40 \times 1.1107 / 0.6862=64.74\, kPa \\& h _2=300.07-100^2 / 2000=295.07 \Rightarrow T _2= 2 9 4 . 7 K , P _{ r 2}=1.0462 \\& P _2=64.74 \times 1.0462 / 1.1107= 6 1 ~ k P a \\& v _2= RT _2 / P _2=0.287 \times 294.7 / 61=1.386 \,m ^3 / kg \\& A _1 / A _2=\left( v _1 / v _2\right)\left( V _2 / V _1\right)=(1.874 / 1.386)(100 / 277.8)= 0 . 4 8 7\end{aligned}

Related Answered Questions

Question: 17.SP.73

Repeat Problem 17.44 assuming a diffuser efficiency of 80%. ...

Verified Answer:

\begin{aligned}& V =1000 \,km / h =277....
Question: 17.CSGP.84

At what Mach number will the normal shock occur in the nozzle of Problem 17.53 if the back pressure is 1.4 MPa? (trial and error on Mx) ...

Verified Answer:

Relate the inlet and exit conditions to the shock ...
Question: 17.CSGP.83

The nozzle in Problem 17.46 will have a throat area of 0.001272 m² and an exit area 2.896 times as large. Suppose the back pressure is raised to 1.4 MPa and that the flow remains isentropic except for a normal shock wave. Verify that the shock mach number (Mx) is close to 2 and find the exit mach ...

Verified Answer:

(a) From Table A.12:    M_E=2.6 [la...
Question: 17.CSGP.82

Atmospheric air is at 20°C, 100 kPa with zero velocity. An adiabatic reversible compressor takes atmospheric air in through a pipe with cross-sectional area of 0.1 m² at a rate of 1 kg/s. It is compressed up to a measured stagnation pressure of 500 kPa and leaves through a pipe with cross-sectional ...

Verified Answer:

C.V. compressor out to standing air and exit to st...
Question: 17.CSGP.81

A convergent nozzle is used to measure the flow of air to an engine. The atmosphere is at 100 kPa, 25°C. The nozzle used has a minimum area of 2000 mm2 and the coefficient of discharge is 0.95. A pressure difference across the nozzle is measured to 2.5 kPa. Find the mass flow rate assuming ...

Verified Answer:

Assume  \mathbf{V} _{ i } \cong 0, \quad v ...
Question: 17.CSGP.80

The coefficient of discharge of a sharp-edged orifice is determined at one set of conditions by use of an accurately calibrated gasometer. The orifice has a diameter of 20 mm and the pipe diameter is 50 mm. The absolute upstream pressure is 200 kPa and the pressure drop across the orifice is 82 mm ...

Verified Answer:

\begin{aligned}& \Delta P =82 \times 10...
Question: 17.CSGP.79

A convergent nozzle with exit diameter of 2 cm has an air inlet flow of 20°C, 101 kPa (stagnation conditions). The nozzle has an isentropic efficiency of 95% and the pressure drop is measured to 50 cm water column. Find the mass flow rate assuming compressible adiabatic flow. Repeat calculation for ...

Verified Answer:

Convert ΔP to kPa: \begin{aligned}& \De...
Question: 17.CSGP.78

Steam at 800 kPa, 350°C flows through a convergent-divergent nozzle that has a throat area of 350 mm². The pressure at the exit plane is 150 kPa and the exit velocity is 800 m/s. The flow from the nozzle entrance to the throat is reversible and adiabatic. Determine the exit area of the nozzle, the ...

Verified Answer:

\begin{aligned}& h _{ o 1}=3161.7 \,kJ ...
Question: 17.CSGP.77

Steam at a pressure of 1 MPa and temperature of 400°C expands in a nozzle to a pressure of 200 kPa. The nozzle efficiency is 90% and the mass flow rate is 10 kg/s. Determine the nozzle exit area and the exit velocity. ...

Verified Answer:

First do the ideal reversible adiabatic nozzle [l...
Question: 17.CSGP.76

Air is expanded in a nozzle from 700 kPa, 200°C, to 150 kPa in a nozzle having an efficiency of 90%. The mass flow rate is 4 kg/s. Determine the exit area of the nozzle, the exit velocity, and the increase of entropy per kilogram of air. Compare these results with those of a reversible adiabatic ...

Verified Answer:

\begin{aligned}& T _{2 s }= T _1\left( ...