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Chapter 6: Problem 80

Calculate nondimensional additive drag, \(D_{\text {nda }} / P_{0} A_{1}\), for a subsonic inlet at cruise condition, \(M_{0}=0.8, A_{0} / A_{1}=\) \(0.835 .\)

Short Answer

Expert verified
The nondimensional drag is approximately 0.0088

Step by step solution

01

Definition of Nondimensional Additive Drag

Nondimensional additive drag, represented as \(D_{\text {nda }} / P_{0} A_{1}\), is a parameter used to determine the aerodynamic efficiency of an aircraft. It's given by the formula \(D_{\text {nda }} / P_{0} A_{1} = 0.075(M_0)^{1.5}(1-A_{0} / A_{1})\), where \(M_0\) is the Mach number and \(A_{0}\) is the area of the subsonic inlet and \(A_{1}\) is the reference area.
02

Substituting The Given Values into The Equation

The aircraft is flying at Mach 0.8, and has an area ratio of \(0.835(A_{0}/A_{1})\). Substituting these values into the formula, we get: \(D_{\text {nda }} / P_{0} A_{1} = 0.075*(0.8)^{1.5}(1-0.835)\).
03

Calculating The Nondimensional Additive Drag

Next is to calculate the expression. With help of a calculator, step by step compute: \(0.075*(0.8)^{1.5}(1-0.835) = 0.008788867\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subsonic Inlet
A subsonic inlet is a crucial part of an aircraft's engine system, especially when dealing with flight at speeds below the speed of sound, typically where the Mach number is less than 1. It is designed to efficiently channel air into the engine with minimal energy loss. Here are some important points about subsonic inlets:

  • The primary function is to slow down the air while simultaneously increasing its pressure before it reaches the engine, thereby ensuring the engine operates smoothly and efficiently.
  • Subsonic inlets are shaped to manage airflow changes and reduce drag, maintaining aerodynamic performance during a flight.
  • Design considerations for subsonic inlets include factors like *inlet loss* and *pressure recovery*, where efficient air pressure recovery helps in minimizing engine performance losses.
  • In the given context, the subsonic inlet works with specific conditions such as a Mach number of 0.8, highlighting how inlets are adapted to different flight regimes.
Mach Number
The Mach number, denoted as \( M_0 \), is a dimensionless unit that represents the ratio of the speed of an object moving through a fluid and the local speed of sound in that fluid. Understanding its importance helps in grasping the dynamics involved in flight:

  • A Mach number below 1, as in this case \( M_0 = 0.8 \), indicates subsonic conditions where the flow speed is less than the speed of sound.
  • The Mach number is crucial for indicating changes in compressibility effects on the airflow, impacting things like drag and lift, which are essential for aircraft design.
  • Higher Mach numbers can lead to different fluid dynamics challenges like shock waves and sonic booms, but in subsonic conditions, these are less of an issue.
  • In the formula for nondimensional additive drag, the Mach number helps to predict the drag characteristics by influencing the term \((M_0)^{1.5}\), showing its profound impact on aerodynamic performance.
Aerodynamic Efficiency
Aerodynamic efficiency reflects how effectively an aircraft can convert engine thrust into forward motion while minimizing resistive forces such as drag. It is a measure of performance that integrates various aspects of the aircraft鈥檚 aerodynamics:

  • One of the ways to assess aerodynamic efficiency is through the calculation of drag, including nondimensional parameters like our focus鈥�*nondimensional additive drag*.
  • The formula \(D_{\text{nda}} / P_0 A_1 = 0.075(M_0)^{1.5}(1-A_0/A_1)\) encapsulates the relationship between the Mach number and other inlet characteristics, assisting in the measurement of efficiency losses due to drag.
  • Aerodynamic efficiency impacts fuel consumption, range, and speed, making it a critical factor in the design and operation of aircraft.
  • Enhancing aerodynamic efficiency often involves optimizing shapes, materials, and systems to reduce the drag force, thus allowing for better performance at various speeds.

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Most popular questions from this chapter

An overexpanded supersonic convergent-divergent nozzle has an inlet total pressure of \(p_{\mathrm{t} 7}=213 \mathrm{kPa}\) and an area ratio of \(A_{9} / A_{8}=3.02\). The ratio of specific heats is \(\gamma=1.3\) and \(\mathrm{c}_{\mathrm{p}}=1,250 \mathrm{~J} / \mathrm{kg} . \mathrm{K}\). Neglecting losses in the nozzle and assuming ambient static pressure is \(p_{0}=25.2 \mathrm{kPa}\), calculate (a) nozzle exit Mach number \(M_{9}\) (b) nozzle exit (static) pressure, \(p_{9}\) (c) the oblique shock wave angle, \(\beta\) in degrees

A convergent-divergent nozzle has an area ratio of \(A_{9} / A_{8}=4.2\). The nozzle pressure ratio is \(\mathrm{NPR}=20\) with \(\gamma=1.3 .\) Assuming that the flow in the CD nozzle is isentropic, calculate (a) exit Mach number, \(M_{9}\) (b) ratio of exit static to inlet total pressure, \(p_{9} / p_{9}\) (c) what kind of wave will form at the nozzle exit? Why? (d) what is the static pressure ratio across the wave?

A supersonic inlet creates two oblique shocks and a normal shock, as shown. The normal component of Mach number to these shocks is \(1.3\), for each of the three shocks. For \(\gamma=1.4\), calculate (a) the total pressure recovery of the shock system (b) Mach number at the entrance to the subsonic diffuser, \(M_{3}\)

A subsonic inlet is cruising at \(M_{0}=0.85\) and the capture area ratio \(A_{0} / A_{1}\) is \(0.90\) (as shown). For an altitude pressure of \(p_{0}=25 \mathrm{kPa}\), the temperature of \(T_{0}=-25^{\circ} \mathrm{C}\), and inlet area \(A_{1}=3 \mathrm{~m}^{2}\), calculate (a) the inlet Mach number \(M_{1}\) (b) the inlet additive drag \(D_{\text {asd }}(\mathrm{N})\) (c) inlet mass flow rate \(m(\mathrm{~kg} / \mathrm{s})\) (d) the inlet ram drag \(D_{\text {ram }}(\mathrm{kN})\) (e) engine face area \(A_{2}\), if \(M_{2}=0.5\) (assuming \(\pi_{\mathrm{d}}=\) \(0.99\) )

A variable-geometry supersonic convergentdivergent inlet is to be designed for an isentropic operation (in the started mode) at \(M_{\mathrm{D}}=2.6\). Calculate (a) the inlet design contraction ratio \(A_{1} / A_{\text {th }}\) (b) the percentage opening of the throat \(\left(A_{\mathrm{th}}^{\prime}-A_{\mathrm{th}}\right) / A_{\mathrm{th}}\) needed to start the inlet (c) the throat Mach number in the open position, \(M_{\text {th }}^{\prime}\)
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