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Chapter 6: Q. 34 (page 155)

A medium-sized jet has a 3.8mdiameter fuselage and a loaded mass of 85,000kg.The drag on an airplane is primarily due to the cylindrical fuselage, and aerodynamic shaping gives it a drag coefficient of 0.37. How much thrust must the jet’s engines provide to cruise at 230m/sat an altitude where the air density is 1.0kg/m3?

Short Answer

Expert verified

The required thrust provided by jet engines must be110.88kN.

Step by step solution

01

Given information.

Diameter (D) = 3.8m, mass (m) = localid="1647936940605" 85,000kg, drag coefficient (C) = 0.37, velocity (v) = 230m/s, air density (ρ)= 1kg/m3.

02

Calculation

Considering equilibrium the net force will be zero, so the force of thrust must be equal in magnitude to the force of drag.

Fthrust=Fdrag.=12ρCAv2.

localid="1648476595293" A=π×D24.=π×(3.8m)24.=11.33m2.

03

Continuation of calculation 

Here on substitution we get,

Fthrust=Fdrag.=12ρCAv2.

=12×(1.0kg/m3)×(0.37)×(11.33m2)×(230m/s)2.=110.88kN.

Therefore, the thrust is 110.88kN.

04

Final answer

The thrust provided by jet engines must be110.88kN.

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