Which of the following are compressible flows? a) A weather balloon rises at 5 m/s from sea level to an altitude of more than 15 km. b) Water flows through the nozzle of a water jet cutter and the gage pressure drops from 100 MPa to zero. c) The piston of an internal combustion engine moves at 15

Question

Which of the following are compressible flows? a) A weather balloon rises at 5 m/s from sea level to an altitude of more than 15 km. b) Water flows through the nozzle of a water jet cutter and the gage pressure drops from 100 MPa to zero. c) The piston of an internal combustion engine moves at 15 m/s and compresses air and gaseous fuel from 40 kPa to 1300 kPa. d) Liquid nitrogen at 100 kPa with density 807 kg/m³ evaporates from a stationary dewar in a 1 m/s airflow to become nitrogen gas with density 1.16 kg/m³. e) A 1.0 MPa compression wave travels at 1.0 km/s into air at 15°C and 1.0 atm.

Accepted Answer

The essential feature of compressible flow (as defined in this section) is coupling between fluid velocity, pressure, and density. For a), the pressure and density of the air outside the balloon and the helium inside it will vary by a factor of eight before the balloon reaches an altitude of 15 km. However, such changes primarily depend on altitude and are largely independent of the low-Mach number rise speed, so this is not a compressible flow. For b), the water experiences an enormous pressure drop and accelerates to more than 400 m/s. However, the density change is modest, as can be estimated from a discretized evaluation of (1.25) using [latex]C_{ ext {water }}[/latex] ∼ 1480 m/s:

[latex]c^2 \equiv(\partial p / \partial ho)_s[/latex]. (1.25)

[latex]\Delta ho / ho \cong \Delta p / ho c^2 \cong 100 MPa /\left(1000 \mathrm{kgm}^{-3} \cdot\left(1480 \mathrm{ms} ^{-1} ight)^2 ight)=0.046[/latex].

This flow might qualify as compressible depending on the level of accuracy that is sought. For c), the pressure and density of the combustion gases rise by factors of more than 30 and 10, respectively. However, like the weather balloon, such changes primarily depend on piston location and are largely independent of the low-Mach number piston speed, so this is not a compressible flow. For d), the nitrogen accelerates to 1 m/s and its density drops by a factor ∼700, but there are no significant pressure variations, so this flow is not compressible. For e), the wave speed is supersonic and the increase in air pressure (a factor of ∼10) and density (a factor of ∼4) across the wave are significant. This is a compressible flow.

Question 15.1: Which of the following are compressible flows? a) A weather ...

Related Answered Questions

Verified Answer:

A normal shock wave forms just ahead of a bullet as it travels at 750 m/s through still air at 100 kPa and 295 K. What are the pressure, temperature, and density of the air immediately behind the shock wave? ...

Verified Answer:

Verified Answer:

Verified Answer:

Determine the lift and drag coefficients of an infinitely-thin but mildly-cambered airfoil at zero angle of attack in a horizontal supersonic flow at speed M∞. ...

Verified Answer:

Consider a quiescent inviscid perfect gas to the right of an ideal piston in a long duct with constant cross-section. At t = t1, the piston located at x = cot1 accelerates to the left until it reaches x = 0, then its speed remains constant. The piston’s trajectory, xp(t), is such that the C+ ...

Verified Answer:

Verified Answer:

Verified Answer: