Solved: Dimensions of b/a in Pressure Equation

In summary, the given equation for pressure (P) of a particle is P = b - t^2 / ax, where b and (- t^2 / ax) must have identical units and the same units as P in order for the equation to be valid.
  • #1
physics kiddy
135
1

Homework Statement



Assuming that Pressure (P) of a particle is given by

P = b - t^2 / ax

where t = time, x = position
Find the dimension of b/a.


Homework Equations







The Attempt at a Solution



Using dimensional homogenity, I know that b represents time interval.
 
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  • #2
physics kiddy said:

Homework Statement



Assuming that Pressure (P) of a particle is given by

P = b - t^2 / ax

Is this (b-t2)/ax or b - (t2/ax)?

If it is the first, there is a subtraction of two quantities. Subtraction of what two quantities gives pressure? What does that tell you about b? and (t2/ax)?

If it's the second, what should be the dimension of b so that (t2/ax) can be subtracted from it? (apples and oranges? or, apples and apples? :wink:)
 
  • #3
Assuming you have represented the formula correctly ...
Using dimensional homogenity, I know that b represents time interval.
I don't think so.
qcPcD.gif
...

your equation shows P comprising the sum of two components: b and (- t^2 / ax). Those two components must have identical units otherwise you couldn't add them, and what's more, they must have the same units as P.

P = b - t^2 / ax
 

Related to Solved: Dimensions of b/a in Pressure Equation

1. What is the pressure equation and how is b/a related to it?

The pressure equation is an equation that relates the force applied to a surface to the area over which it is distributed. It is written as P = F/A, where P is pressure, F is force, and A is area. The b/a in the pressure equation refers to the ratio of the width (b) to the length (a) of the surface over which the force is applied.

2. Why is it important to know the dimensions of b/a in the pressure equation?

Knowing the dimensions of b/a in the pressure equation is important because it allows us to understand how the pressure changes with the size and shape of the surface. It also helps us determine the theoretical limit of pressure that can be applied to a surface before it fails.

3. How does changing the dimensions of b/a affect the pressure on a surface?

Changing the dimensions of b/a can have a significant impact on the pressure on a surface. As b/a increases, the pressure decreases, and as b/a decreases, the pressure increases. This is because a larger surface area (a larger b/a ratio) means that the force is distributed over a larger area, resulting in lower pressure, and vice versa.

4. Can the dimensions of b/a be greater than 1 in the pressure equation?

Yes, the dimensions of b/a can be greater than 1 in the pressure equation. This means that the width of the surface is greater than the length. In this case, the pressure on the surface would be lower compared to a surface with a b/a ratio of less than 1.

5. How can the dimensions of b/a be determined experimentally?

The dimensions of b/a can be determined experimentally by measuring the width and length of the surface and then calculating the ratio between the two. This can be done using a ruler or calipers to measure the dimensions of the surface. Additionally, various techniques such as strain gauges or pressure sensors can be used to directly measure the force and area and calculate the b/a ratio.

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