# Units involving metres

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• richard9678
In summary, the conversation discusses stress measured in Pascals and how it relates to the Hall-Petch equation. The equation includes a constant, k, which is given in units of MN m-3/2. There is some confusion about the units and potential errors in the text, but it is ultimately determined that the units for k are MPa-m1/2.

#### richard9678

Hi. Stress is measured on Pascals. It's force divided by area. Area of course is m x m. So when stress is given it's in units of MN / m2 or MN m-2.

Okay. I'm looking at something called the Hall Petch equation. There a constant in it labelled k.

In an example, k is given as 0.45 MN m-3/2

Does this make any sense or is there an error with the description of k?

I mean, what is m-3/2? Thanks.

P.S. Possible that there is an error in the text. And that k is MN m1/2. However, if it is, I still don't know what m is as a unit. In other words I know m2 is - square meters.

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The Hall-Petch equation asserts a relation of the form $$(\mathrm{stress}) = \frac{(\mathrm{coefficient})}{(\mathrm{length})^x}$$ or $$(\mathrm{coefficient}) = (\mathrm{stress})(\mathrm{length})^x.$$ It follows that in SI units the coefficient is measured in units of $\mathrm{Pa}\,\mathrm{m}^x$ or $\mathrm{N}\,\mathrm{m}^{x-2}$. $x$ need not be an integer.

richard9678 said:
Hi. Stress is measured on Pascals. It's force divided by area. Area of course is m x m. So when stress is given it's in units of MN / m2 or MN m-2.

Okay. I'm looking at something called the Hall Petch equation. There a constant in it labelled k.

In an example, k is given as 0.45 MN m-3/2

Does this make any sense or is there an error with the description of k?

I mean, what is m-3/2? Thanks.

P.S. Possible that there is an error in the text. And that k is MN m1/2. However, if it is, I still don't know what m is as a unit. In other words I know m2 is - square meters.
In fracture mechanics, the stress intensity factor for different types of flaws is expressed in units of MPa-m1/2.

https://en.wikipedia.org/wiki/Fracture_mechanics

## 1. What is the basic unit of measurement for length in the metric system?

The basic unit of measurement for length in the metric system is the metre (m). It is equivalent to approximately 3.28 feet.

## 2. How many centimetres are in a metre?

There are 100 centimetres in one metre. This makes it easy to convert between the two units by simply moving the decimal point.

## 3. What is the prefix used to represent one thousandth of a metre?

The prefix used to represent one thousandth of a metre is milli-. This means that one millimetre (mm) is equal to 0.001 metres.

## 4. How is the metre defined in the International System of Units (SI)?

The metre is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. This definition was adopted in 1983 by the General Conference on Weights and Measures.

## 5. Why is the metre considered a more practical unit of measurement compared to the imperial system?

The metre is considered a more practical unit of measurement compared to the imperial system because it is based on a decimal system, making it easier to convert between units. It is also a universal unit, used by the majority of countries in the world, making it easier to communicate and compare measurements internationally.