The viscosity of air is independent of pressure for...

The viscosity of air is independent of pressure for temperature below 3000K. In this temperature range, the Sutherland's equation is used to calculate the coefficient of viscosity as the following: $$\mu = C_1 \frac{T^{1.5}}{T + C_2}$$ where T is in units of K and $\mu$ is in units of kg/(m⋅s). The parameters $C_1 = 1.458 \times 10^{-6}$, and $C_2 = 110.4$. Calculate: (1) The viscosity of air at sea level where the temperature is 288.15K (2) The viscosity of air at altitude 10km when the temperature is 223K. Also, we know the speed of sound $c = \sqrt{\gamma RT}$, where $\gamma = 1.4$ is the ratio of the specific heats of air, and $R = 287$J/(kg⋅K) is the gas constant of air. Calculate: (3) Speed of sound at sea level, where temperature is 288.15K (4) Speed of sound at altitude 10km.

Transcript

00:01 So in this question, what we are given is that it says that for the air, right, for the air at standard atmospheric pressure, atmospheric pressure, right? the values of the constants that they appear in the sutherland equation, right, they are given to us.

00:36 And this equation is 1 .10, right? so these values are, we have c that is equal to 1 .458 into 10 raised to power negative 6 kilogram, right? and the value of s is 1 .10 .4 kilo, right? now, in the statement it asks us to use these values.

01:07 In order to predict the viscosity of air at temperatures 10 degrees centigrade and 90 degrees centigrade, right? and then we need to compare them with the values that are given in the table, right? so let's start the solution.

01:28 Now the solution for this question, it's very simple, right? so first of all, what we're going to do is that we are going to start by converting the temperatures from degrees to calvin right so let t1 be equal to 10 degrees centigrade right so when we convert it into calvin we get that it is equal to 283 .15 calvin right and let the other temperature be t do right and it's equal to 90 degrees centigrade um and when you converted we get that it is equal to 363 .15 calvin right now what we are going to do from here is that we are going to calculate viscosity directly from the southern lands formula.

02:15 So we have viscosity at 10 degrees centigrade that is approximately equal to c times t raised to power 3 divided by 2.

02:28 And that is divided by d plus s.

02:33 So when you plug in the values, right? so you get that it's 1 .458 into 10.

02:43 To power negative 6 right and over here we have 283 .15 kelvin ways to power 3 by 2 right and in the denominator we have 283 .15 kelvin plus 110 .4 calvin right so when you calculated you get that the viscosity at 10 degree for air it's approximately equal to 2.

03:19 2 .10...

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