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Use dimensional analysis to show Q=kpr⁴/ml?​

User Visme
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Answer:

Dimensional analysis is a powerful tool used in physics and engineering to analyze and verify the correctness of equations. Let's break down the given equation Q = kpr⁴/ml using dimensional analysis:

On the left-hand side (LHS), we have Q, which represents a quantity that we need to determine its dimensions.

On the right-hand side (RHS), we have k, a constant that doesn't have any units associated with it.

Next, let's break down the dimensions of each term on the RHS:

pr⁴:

- p represents pressure with units of force per unit area (N/m² or Pa).

- r represents distance with units of meters (m).

- r⁴ represents distance raised to the power of four, so its units will be (m^4).

ml:

- m represents mass with units of kilograms (kg).

- l represents length with units of meters (m).

- Therefore, ml represents volume with units of cubic meters (m³).

So, combining the dimensions on the RHS, we have:

kpr⁴/ml = (dimensionless) * (m) * (m^4) / (m³)

Simplifying the equation further:

kpr⁴/ml = (m^(4+1-3))

kpr⁴/ml = (m²)

Comparing the LHS and the RHS, we see that the dimensions of Q are (m²). Therefore, the equation Q = kpr⁴/ml is dimensionally consistent.

By utilizing dimensional analysis, we can confirm that the equation is valid and the dimensions on both sides of the equation match, indicating a correct relationship between the variables.

User John Whish
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