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
tangare [24]
3 years ago
6

Determine the power that needs to besupplied by the fanifthe desired velocity is 0.05 m3/s and the cross-sectional area is 20 cm

Physics
1 answer:
Mariulka [41]3 years ago
5 0

Answer:

A fan with an energy efficiency of 30 % would need 62.5 watts to bring a desired volume flow of 0.05 cubic meters per second through a cross-sectional area of 20 square centimeters.

Explanation:

Complete statement is: <em>Determine the power that needs to besupplied by the fan if the desired velocity is 0.05 cubic meters per second and the cross-sectional area is 20 square centimeters.</em>

From Thermodynamics and Fluid Mechanics we know that fans are devices that work at steady state which accelerate gases (i.e. air) with no changes in pressure. In this case, mechanical rotation energy is transformed into kinetic energy. If we include losses due to mechanical friction, the Principle of Energy Conservation presents the following equation:

\eta\cdot \dot W = \dot K

\dot W = \frac{\dot K}{\eta} (Eq. 1)

Where:

\eta - Efficiency of fan, dimensionless.

\dot W - Electric power supplied fan, measured in watts.

\dot K - Rate of change of kinetic energy of air in time, measured in watts.

From definition of kinetic energy, the equation above is now expanded:

\dot W = \frac{\rho_{a}\cdot \dot V}{2\cdot \eta}\cdot \left(\frac{\dot V}{A_{s}} \right)^{2} (Eq. 2)

Where:

\rho_{a} - Density of air, measured in kilograms per cubic meter.

\dot V - Volume flow, measured in cubic meters per second.

A_{s} - Cross-sectional area of fan, measured in square meters.

If we know that \rho_{a} = 1.20\,\frac{kg}{m^{3}}, \dot V = 0.05\,\frac{m^{3}}{s}, \eta = 0.3 and A_{s} = 20\times 10^{-4}\,m^{2}, the power needed to be supplied by the fan is:

\dot K = \left[\frac{\left(1.20\,\frac{kg}{m^{3}} \right)\cdot \left(0.05\,\frac{m^{3}}{s} \right)}{2\cdot (0.3)} \right]\cdot \left(\frac{0.05\,\frac{m^{3}}{s} }{20\times 10^{-4}\,m^{2}} \right)^{2}

\dot K = 62.5\,W

A fan with an energy efficiency of 30 % would need 62.5 watts to bring a desired volume flow of 0.05 cubic meters per second through a cross-sectional area of 20 square centimeters.

You might be interested in
Can work done=mass*acceleration*displacement(work=m*a*s)
Airida [17]

no, work is = force * distance or displacement


5 0
3 years ago
According to the text, there is no energy shortage now, nor will there ever be. what reason (s) is given to support this stateme
Bas_tet [7]
The reason why there is no energy shortage nor will there ever be is because energy is being preserved and conserved and only changes form. It never gets lost or increased.
8 0
2 years ago
What makes the planets gravity?
anyanavicka [17]
The presence of mass makes gravity. Doesn't matter whether it's a planet, a black hole, a puppy, or a speck of dust.
3 0
2 years ago
G a person of mass 100 kg is riding an elevator which was initially moving up with a velocity of 3 m/s. over a distance of 4 m t
andriy [413]
E=mc² where c is speed of the light
3 m/s more andmore less than speed of the light. So mass of the person still 100 kg
3 0
3 years ago
A child of mass 27 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and
snow_tiger [21]

Answer:

The magnitude of the rate of change of the child's momentum is 794.11 N.

Explanation:

Given that,

Mass of child = 27 kg

Speed of child in horizontal = 10 m/s

Length = 3.40 m

There is a rate of change of the perpendicular component of momentum.

Centripetal force acts always towards the center.

We need to calculate the magnitude of the rate of change of the child's momentum

Using formula of momentum

\dfrac{dp}{dt}=F

\dfrac{dP}{dt}=\dfrac{mv^2}{r}

Put the value into the formula

\dfrac{dP}{dt}=\dfrac{27\times10^2}{3.40}

\dfrac{dP}{dt}=794.11\ N

Hence, The magnitude of the rate of change of the child's momentum is 794.11 N.

7 0
3 years ago
Other questions:
  • Water that soaks into Earth may become _____ under the surface.
    13·1 answer
  • Which of the following is not a unit used to measure pressure?
    10·2 answers
  • When steam condenses 1. All of these occur. 2. None of these occur. 3. molecules move closer together. 4. it changes from the ga
    13·2 answers
  • When carrying extra weight, the space formed between the top of your head and the two axles of the motorcycle is referred to as
    10·1 answer
  • The rate constant for this second‑order reaction is 0.760 M−1⋅s−1 at 300 ∘C. A⟶products How long, in seconds, would it take for
    7·1 answer
  • The work done by static friction can be : a. Zero
    14·1 answer
  • Will mark the brainiest
    13·2 answers
  • What causes the movement of deep ocean currents?
    14·1 answer
  • The object was thrown vertically upwards at a speed of 30 m / s. How high does the body go?
    9·1 answer
  • A police officer uses a radar gun to determine the speed of a car. A specialized radar gun uses ultraviolet light to determine t
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!