Why does the outlet pressure in a hair dryer remain constant?

In summary, the flow rate and velocity of air at the exit are decreasing as the outlet temperature is increased. This is due to the fact that the velocity is determined by the time the air has to absorb heat, which gets shorter as the temperature is increased.
  • #1
gfd43tg
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Homework Statement


A hair dryer is basically a duct in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it to flow over the resistors where it is heated. Air enters a 900-W hair dryer at 100 kPa and 25° C, and leaves at 50° C. The cross-sectional area of the hair dryer at the exit is 60 cm^2. Neglecting the power consumed by the fan and the heat losses through the walls of the hair dryer, determine (a) the volume flow rate of air at the inlet, and (b) the velocity of the air at the exit.

Answers: (a) 0.0306 m/s, (b) 5.52 m/s

Homework Equations


The Attempt at a Solution


I already have solved this problem, but I stepped it up a notch and am now playing with MATLAB. I am varying the inlet and outlet temperatures to see how the behavior of the flow rate and velocity of air at the exit will change when I change the parameters.

One preliminary question I want to ask is why is it that the outlet pressure is assumed to be the same as the inlet pressure?

The first thing I did was vary the outlet temperature to see the effect of the velocity of air. I see in the plot that I have a ''1/x'' behavior, which is intriguing to me. I wonder, how can it be that as I increase the outlet temperature, the velocity in the exit is actually decreasing, and then plateaus?

Same thing for inlet volumetric flow rate, why the negative exponential behavior? Shouldn't hotter air travel faster??

Then I played with the inlet temperature vs. outlet velocity, and got extremely weird behavior. I suspect the reason for this is because I was varying the temperature without varying the pressure, and that would go against the degrees of freedom. Anytime I messed with the inlet temperature, it is clearly something going wrong.

Basically I'm just wondering what the physical reason is for the behavior I am getting as shown by my plots.

Lastly, are there any other suggestions for parameters to play with and see the effect for the purpose of understanding the physics of this problem?
 

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  • #2
I just did a similar problem and plotted the mass flow rate vs. outlet temperature for a given ##\dot{Q}##, and I think I can explain it. So if the air was flowing through the hair dryer very slowly, it will have more residence time inside the dryer and hence absorb more heat, and exit at a higher temperature.

When it is at a faster flow rate, it has less time to absorb heat, and hence leaves at a lower temperature. That is why the mass flow rate is very slow for a high outlet temperature, as seen in this graph. I think it is probably easier to conceptualize what would happen if you slowed down the flow rate, rather than try to think how the flow rate would be affected if you increased the temperature.

I think what I was hypothesizing was the fact that somehow increasing the outlet temperature has an effect on the mass flow rate intrinsically, but they are both variables that can be controlled. I am having some trouble exactly articulating this point though, so maybe someone can chime in.
 
  • #3
There was discussion on hairdriers a year or two back. IIRC I observed that increasing the heating while maintaining fan speed setting fixed resulted in no discernible change in output volumetric flow. This was a surprising finding.
 

What is air flow?

Air flow refers to the movement of air from one place to another. In the context of a hair dryer, it is the movement of air from the back of the hair dryer, through its internal components, and out through the nozzle.

How does a hair dryer create air flow?

A hair dryer uses an electric motor to power a fan that draws in air from the back of the hair dryer. The air is then forced through the heating element, which heats it up, and then out through the nozzle at a high velocity.

Why is air flow important in a hair dryer?

Air flow is important in a hair dryer because it helps to dry and style hair. The movement of air helps to evaporate moisture from wet hair, and the high velocity of the air helps to shape and control the hair as it is blown out of the nozzle.

Can the air flow in a hair dryer be adjusted?

Yes, most hair dryers have multiple speed and heat settings that allow the user to adjust the air flow. Lower speeds and cooler temperatures are typically used for more delicate hair or for styling, while higher speeds and hotter temperatures are used for faster drying.

How does air flow affect the performance of a hair dryer?

The air flow in a hair dryer can greatly affect its performance. A hair dryer with a strong and consistent air flow will dry hair faster and more efficiently, while a weak or inconsistent air flow may result in longer drying times or uneven drying. It can also impact the overall styling capabilities of the hair dryer.

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