Understanding Dimensions of Velocity Gradient - Testbook
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Breaking Down the Dimensional Formula of Velocity Gradient
When it comes to understanding the concept of velocity gradient, we need to first look at its dimensional formula. This is represented as:
[M0 L0 T-1]
In this formula, the symbols M, L, and T stand for:
- M = Mass
- L = Length
- T = Time
How to Derive the Dimensional Formula of Velocity Gradient
The concept of velocity gradient can be broken down into velocity multiplied by the inverse of distance. Mathematically, this is represented as:
Velocity Gradient = velocity × [distance]-1
The dimensional formula of velocity is given by [M0 L1 T-1], and the dimensional formula of distance is [M0 L1 T0].
If we substitute these values into our original equation, we get:
Velocity Gradient = velocity × [distance]-1 = [M0 L1 T-1] × [M0 L1 T0]-1 = [M0 L0 T-1]
Therefore, the dimensional representation of velocity gradient is [M0 L0 T-1].
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Frequently Asked Questions
What is the dimensional formula of velocity gradient?
The dimensional formula of velocity gradient is [M^0 L^0 T^-1].
How is the dimensional formula of velocity gradient derived?
The formula is derived using the dimensional formulas of velocity and distance. Velocity Gradient = velocity x [distance]^-1. Substituting the dimensional formulas of velocity and distance we get [M^0 L^0 T^-1].
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