1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gelneren [198K]
3 years ago
12

Air enters a nozzle steadily at 2.21 kg/m3 and 20 m/s and leaves at 0.762 kg/m3 and 150 m/s. If the inlet area of the nozzle is

60 cm2, determine (a) the mass flow rate through the nozzle, and (b) the exit area of the nozzle
Physics
2 answers:
zalisa [80]3 years ago
8 0

a) Mass flow rate through the nozzle: 0.265 kilograms per second, b) Exit area of the nozzle: 23.202 square centimeters.

We determine the Mass Flow Rate through the nozzle and the Exit Area of the nozzle by means of the Principle of Mass Conservation. A nozzle is a device that works at Steady State, so that Mass Balance can be reduced into this form:

\dot m_{in} = \dot m_{out} (1)

Where:

\dot m_{in} - Inlet mass flow, in kilograms per second.

\dot m_{out} - Outlet mass flow, in kilograms per second.

Given that air flows at constant rate, we expand (1) by dimensional analysis:

\rho_{in} \cdot A_{in}\cdot v_{in} = \rho_{out}\cdot A_{out}\cdot v_{out} (2)

Where:

\rho_{in}, \rho_{out} - Air density at inlet and outlet, in kilograms per cubic meter.

A_{in}, A_{out} - Inlet and outlet area, in square meters.

v_{in}, v_{out} - Inlet and outlet velocity, in meters per second.

a) If we know that \rho_{in} = 2.21\,\frac{kg}{m^{3}}, A_{in} = 60\times 10^{-4}\,m^{2} and v_{in} = 20\,\frac{m}{s}, then the mass flow rate through the nozzle is:

\dot m = \rho_{in}\cdot A_{in}\cdot v_{in}

\dot m = \left(2.21\,\frac{kg}{m^{3}} \right)\cdot (60\times 10^{-4}\,m^{2})\cdot \left(20\,\frac{m}{s} \right)

\dot m = 0.265\,\frac{kg}{s}

The mass flow rate through the nozzle is 0.265 kilograms per second.

b) If we know that \rho_{in} = 2.21\,\frac{kg}{m^{3}}, A_{in} = 60\times 10^{-4}\,m^{2}, v_{in} = 20\,\frac{m}{s}, \rho_{out} = 0.762\,\frac{kg}{m^{3}} and v_{out} = 150\,\frac{m}{s}, then the exit area of the nozzle is:

\rho_{in} \cdot A_{in}\cdot v_{in} = \rho_{out}\cdot A_{out}\cdot v_{out}

A_{out} = \frac{\rho_{in}\cdot A_{in}\cdot v_{in}}{\rho_{out}\cdot v_{out}}

A_{out} = \frac{\left(2.21\,\frac{kg}{m^{3}} \right)\cdot (60\times 10^{-4}\,m^{2})\cdot \left(20\,\frac{m}{s} \right)}{\left(0.762\,\frac{kg}{m^{3}} \right)\cdot \left(150\,\frac{m}{s} \right)}

A_{out} = 2.320\times 10^{-3}\,m^{2}

A_{out} = 23.202\,cm^{2}

The exit area of the nozzle is 23.202 square centimeters.

saveliy_v [14]3 years ago
5 0

Answer:

a) The mass flow rate through the nozzle is 0.27 kg/s.

b) The exit area of the nozzle is 23.6 cm².

Explanation:

a) The mass flow rate through the nozzle can be calculated with the following equation:

\dot{m_{i}} = \rho_{i} v_{i}A_{i}

Where:

v_{i}: is the initial velocity = 20 m/s

A_{i}: is the inlet area of the nozzle = 60 cm²  

\rho_{i}: is the density of entrance = 2.21 kg/m³

\dot{m} = \rho_{i} v_{i}A_{i} = 2.21 \frac{kg}{m^{3}}*20 \frac{m}{s}*60 cm^{2}*\frac{1 m^{2}}{(100 cm)^{2}} = 0.27 kg/s  

Hence, the mass flow rate through the nozzle is 0.27 kg/s.

b) The exit area of the nozzle can be found with the Continuity equation:

\rho_{i} v_{i}A_{i} = \rho_{f} v_{f}A_{f}

0.27 kg/s = 0.762 kg/m^{3}*150 m/s*A_{f}

A_{f} = \frac{0.27 kg/s}{0.762 kg/m^{3}*150 m/s} = 0.00236 m^{2}*\frac{(100 cm)^{2}}{1 m^{2}} = 23.6 cm^{2}

Therefore, the exit area of the nozzle is 23.6 cm².

I hope it helps you!                                                                  

You might be interested in
Shari uses the data in the table to predict how her weight on Venus would compare with her weight on Earth.
spin [16.1K]

Answer :  <em>Her weight is lower on Venus because the acceleration due to gravity is lower.</em>

Explanation :

Venus is also called as Earth's twin. This is because both the mass and the size of Earth and Venus are almost same. The acceleration due to gravity on earth is 9.8\ m/s^2 while on Venus is 8.87\ m/s^2.

So, when Shari measure her weight on Venus she found her weight is lower on Venus. This is because the acceleration due to gravity is lower on the surface of Venus as compared to the Earth.

Since,    w=mg

i.e. weight depends on g.

<em>So, correct prediction is (b)</em>

3 0
3 years ago
Read 2 more answers
How is heat converted into work in a steam engine?
Dmitry_Shevchenko [17]
In an extremely simplified explanation,
What happens is that the steam (heat) that is generated by the burning of coal is used to rotate the motor of the steam engine.
8 0
3 years ago
Look at the graph. What is the slope of the line?
NeTakaya

For the first hour, the slope is zero.

After that, the slope is -2 miles per hour.

7 0
2 years ago
According to Bernoulli's equation, the pressure in a fluid will tend to decrease if its velocity increases. Assuming that a wind
Pie

Answer:

The pressure drop predicted by Bernoulli's equation for a wind speed of 5 m/s

= 16.125 Pa

Explanation:

The Bernoulli's equation is essentially a law of conservation of energy.

It describes the change in pressure in relation to the changes in kinetic (velocity changes) and potential (elevation changes) energies.

For this question, we assume that the elevation changes are negligible; so, the Bernoulli's equation is reduced to a pressure change term and a change in kinetic energy term.

We also assume that the initial velocity of wind is 0 m/s.

This calculation is presented in the attached images to this solution.

Using the initial conditions of 0.645 Pa pressure drop and a wind speed of 1 m/s, we first calculate the density of our fluid; air.

The density is obtained to be 1.29 kg/m³.

Then, the second part of the question requires us to calculate the pressure drop for a wind speed of 5 m/s.

We then use the same formula, plugging in all the parameters, to calculate the pressure drop to be 16.125 Pa.

Hope this Helps!!!

7 0
3 years ago
A bicycle takes 8.0 seconds to accelerate at a constant rate from rest to a speed of 4.0 m/s. If the mass of the bicycle and rid
yanalaym [24]
11.0 second hope i helped
6 0
2 years ago
Other questions:
  • Ultraviolet rays from the sun are able to reach Earth's surface because A. They require air to travel through B. They have less
    8·1 answer
  • Which type of light energy found in solar radiation is most likely to reach earth's surface?
    6·2 answers
  • HURRY ! THE BEST I WILL GIVE THE BRAINLIEST​
    8·1 answer
  • How much energy is stored in the electric field of a 50-μm-diameter cell with a 7.0-nm-thick cell wall whose dielectric constant
    6·2 answers
  • Suppose you heat a liquid and then bubbles are produced. With no other evidence, can you tell whether a physical or chemical is
    7·1 answer
  • A skateboader is accelerating forward how would his acceleration change if he had more mass
    14·1 answer
  • PLEASE HELP ASAPPPPPPPPP
    13·1 answer
  • Give an example of speed making a difference in the amount of kinetic energy. Tell how you know that kinetic energy amount is di
    6·2 answers
  • Which symbol and unit of measurement are used for resistance?
    14·2 answers
  • How 2cos theta ×sin theta is =sin2theta
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!