Category Archives: Engineering

Determine the thrust available to propel the cart.

A CO2 cartridge is used to propel a small rocket cart.

Compressed gas, stored at 35 MPa and 20C, is expanded

through a smoothly contoured converging nozzle with 0.5

mm throat diameter. The back pressure is atmospheric.

Calculate the pressure at the nozzle throat. Evaluate the

mass flow rate of carbon dioxide through the nozzle.

Determine the thrust available to propel the cart. How much

would the thrust increase if a diverging section were added to

the nozzle to expand the gas to atmospheric pressure? What

is the exit area? Show stagnation states, static states, and the

processes on a Ts diagram.

Determine the range(s) of inlet stagnation pressures for which the nozzle will be free from normal shocks.

A converging-diverging nozzle, with Ae/At 5 1.633, is

designed to operate with atmospheric pressure at the exit

plane. Determine the range(s) of inlet stagnation pressures

for which the nozzle will be free from normal shocks.

13.106 Air flows through a converging-diverging nozzle with

Ae/At 5 1.87. Upstream, T01 5 240

F and p01 5 100 psia.

The back pressure is maintained at 40 psia. Determine the

Mach number and flow speed in the nozzle exit plane.

Find the range of exit pressures for which the duct exit flow is choked.

Room air is drawn into an insulated duct of constant

area through a smoothly contoured converging nozzle.

Room conditions are T 5 80

F and p 5 14:7 psia. The duct

diameter is D 5 1 in. The pressure at the duct inlet (nozzle

outlet) is p1 5 13 psia. Find (a) the mass flow rate in the duct

and (b) the range of exit pressures for which the duct exit

flow is choked.

*These problems require material from sections that may be omitted without loss of continuity in the text material.

778 Chapter 13 Compressible Flow

Show static and stagnation state points and the process path on a Ts diagram.

Measurements are made of compressible flow in a long

smooth 7.16 mm i.d. tube. Air is drawn from the surroundings

(20C and 101 kPa) by a vacuum pump downstream. Pressure

readings along the tube become steady when the downstream

pressure is reduced to 626 mm Hg (vacuum) or below. For

these conditions, determine (a) the maximum mass flow rate

possible through the tube, (b) the stagnation pressure of the air

leaving the tube, and (c) the entropy change of the air in the

tube. Show static and stagnation state points and the process

path on a Ts diagram.

Determine the pressure in the tank and the temperature, stagnation pressure, and mass flow rate of the outlet flow, if the tube diameter is 0.249 in.

Air flows through a converging nozzle and then a

length of insulated duct. The air is supplied from a tank

where the temperature is constant at 59F and the pressure is

variable. The outlet end of the duct exhausts to atmosphere.

When the exit flow is just choked, pressure measurements

show the duct inlet pressure and Mach number are 53.2 psia

and 0.30. Determine the pressure in the tank and the temperature, stagnation pressure, and mass flow rate of the

outlet flow, if the tube diameter is 0.249 in. Show on a Ts

diagram the effect of raising the tank pressure to 100 psia.

Sketch the pressure distribution versus distance along the

channel for this new flow condition.

Calculate the temperature and stagnation pressure at the choked state in the constant-area duct.

For the conditions of Problem 13.122, find the length,

L, of commercial steel pipe of 2 in. diameter between sections 1 and 2 .

Consider the laboratory Fanno-line flow channel of

Problem 13.123. Assume laboratory conditions are 22.5C

and 760 mm of mercury (uncorrected). The manometer

reading at a pressure tap at the end of the converging nozzle

is 211.8 mm of mercury (gage). Calculate the Mach number

at this location. Determine the duct length required to attain

choked flow. Calculate the temperature and stagnation

pressure at the choked state in the constant-area duct.

Find the mass flow rate in the duct and T2.

Using coordinates T/T* and ðs 2 sÞ=cp, where s* is

the entropy at M 5 1, plot the Fanno line for air flow for

0:1 , M , 3:0.

Air flows through a 40 ft length of insulated constantarea duct with D 5 2.12 ft. The relative roughness is

e=D 5 0:002. At the duct inlet, T1 5 100F and p1 5

17:0 psia. At a location downstream, p2 5 14.7 psia, and the

flow is subsonic. Is sufficient information given to solve for

M1 and M2? Prove your answer graphically. Find the mass

flow rate in the duct and T2.

Find the mass flow rate in the duct and T2.

Using coordinates T/T* and ðs 2 sÞ=cp, where s* is

the entropy at M 5 1, plot the Fanno line for air flow for

0:1 , M , 3:0.

Air flows through a 40 ft length of insulated constantarea duct with D 5 2.12 ft. The relative roughness is

e=D 5 0:002. At the duct inlet, T1 5 100F and p1 5

17:0 psia. At a location downstream, p2 5 14.7 psia, and the

flow is subsonic. Is sufficient information given to solve for

M1 and M2? Prove your answer graphically. Find the mass

flow rate in the duct and T2.

Determine the amount of heat exchange per unit mass to or from the fluid between sections 1 and 2 and the pressure difference, p1 2 p2.

Consider frictionless flow of air in a constant-area

duct. At section 1 , M1 5 0.50, p1 5 1.10 MPa (abs), and

*These problems require material from sections that may be omitted without loss of continuity in the text material.

780 Chapter 13 Compressible Flow

T01 5 333 K. Through the effect of heat exchange, the Mach

number at section 2 is M2 5 0.90 and the stagnation temperature is T02 5 478 K. Determine the amount of heat

exchange per unit mass to or from the fluid between sections

1 and 2 and the pressure difference, p1 2 p2.

Find the rate of heat transfer

Liquid Freon, used to cool electronic components,

flows steadily into a horizontal tube of constant diameter, D 5

0.65 in. Heat is transferred to the flow, and the liquid boils and

leaves the tube as vapor. The effects of friction are negligible

compared with the effects of heat addition. Flow conditions

are shown. Find (a) the rate of heat transfer and (b) the

pressure difference, p1 2 p2.

1 2

Flow D = 0.65 in.

Q

h1 = 25 Btu/lbm

1 = 100 lbm/ft3

m = 1.85 lbm/s •

ρ

h2 = 65 Btu/lbm

2 = 0.840 lbm/ft3 ρ

P13.159