# Calculate Dynamic Viscosity of Air at 4000m Altitude

• es_joe
In summary, the conversation discusses how to calculate the dynamic viscosity of air at high altitudes, specifically at 4000m above sea level with a temperature of 262 kelvin degrees. The recommended method is to use Sutherland's Formula, which takes into account the temperature and uses a constant value for air. The conversation also mentions that the variation in viscosity is minimal at lower pressures, and provides a formula for calculating kinematic viscosity. It is noted that this formula is similar to Sutherland's method. The conversation ends with a question about the variable "rALT," which is likely a factor used in the kinematic viscosity formula.
es_joe
How to calculate the dynamic viscosity of air at high alttitudes,i want to calculate it at hight 4000m abovesea level at that hight the temp. is 262 kelven degrees.

Any thoughts?

Since viscosity is more or less dependent on temperature, I would start with using Sutherland's Formula:

$$\mu = \mu_o \left[ \frac{0.555T_o+C}{.555T+C}\right] \left[\frac{T}{T_o}\right]^{1.5}$$

Where:
$$\mu_o$$= .01827 cP for air (or some known value at a different known temperature)
$$T_o$$= 524.07°R for air (for the viscosity above, different if using a different value)
$$C$$= 120 for air (Sutherland's constant)
$$T$$= absolute temperature (°R)

Crane's states that the variation in viscosity is on the order of 10% when going up to 500 psi. Assuming no wierdness goes on at lower (sub atmospheric) pressures, the variation should be very small when deviating less than 15 psi.

You can then go on and calculate the dynamic viscosity through the relation $$\nu=\frac{\mu}{\rho}$$

Last edited:
According to: http://www.bh.com/companions/034074152X/appendices/data-d/default.htm

Viscosity (kilogram per metre second)

Viscosity is needed to determine kinematic viscosity as shown in the next item.

mALT = (1.458x10-6 x TALT3/2) / TALT + 110.4

where: mALT = viscosity (kg/ms) at altitude (h)

Kinematic Viscosity (square metre per second)

The coefficient of kinematic viscosity is used in determination of Reynolds Number It is evaluated by the ratio:-

nALT = mALT / rALT

where: nALT = coefficient of kinematic viscosity at altitude (m2/s)

It looks like they use a version of Sutherland's method as shown above.

Last edited by a moderator:
what is rALT ?

## 1. What is dynamic viscosity?

Dynamic viscosity is a measure of the resistance of a fluid to flow under an applied force. It is a property that determines how easily a fluid can be deformed or moved.

## 2. How is dynamic viscosity of air at a specific altitude calculated?

The dynamic viscosity of air at a specific altitude can be calculated using the Sutherland's Law of the variation of viscosity with temperature. This equation takes into account the temperature and pressure at the given altitude to calculate the dynamic viscosity.

## 3. Why is it important to calculate the dynamic viscosity of air at a certain altitude?

The dynamic viscosity of air at a certain altitude is important in various engineering and scientific applications, such as in the design of aircrafts and understanding the flow of air in different environments. It also plays a role in weather forecasting and atmospheric studies.

## 4. How does dynamic viscosity of air change with altitude?

The dynamic viscosity of air decreases with increasing altitude. This is because the air at higher altitudes is less dense and therefore has less resistance to flow. This decrease in viscosity can also be attributed to the decrease in temperature with increasing altitude.

## 5. What is the unit of measurement for dynamic viscosity?

The unit of measurement for dynamic viscosity is Pascal-second (Pa·s) in the SI system, or poise (P) in the CGS system.

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