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Question: The SI unit of pressure gradient is: A. \[N{{m}^{-2}}\] B. \[N{{m}^{-1}}\] C. \[Nm\] D. \[N{...

The SI unit of pressure gradient is:
A. Nm−2N{{m}^{-2}}
B. Nm−1N{{m}^{-1}}
C. NmNm
D. Nm−3N{{m}^{-3}}

Explanation

Solution

To solve this question we must know what is the definition of potential gradient. Also, we must have the knowledge of basic dimensions. In this way, we can derive the unit of pressure gradient from its definition. Now, we know that Force is the product of Pressure and area. Therefore, the pressure can be given as Force upon area. So the unit of force is N and the area is meter square. Which makes the unit of pressure as N per meter squared.

Complete step by step answer:
As we know, the gradient of any quantity is the rate change of the quantity with respect to something. So, in this case that makes pressure gradient the rate of change of atmospheric pressure with respect to any horizontal distance at some given time. This means that pressure gradient is a physical quantity that describes in which direction and at what rate the pressure will increase most rapidly around a given location.
So, now we know that pressure gradient is the ratio of pressure to distance. Therefore, by taking ratios of their dimensions we can derive the units for pressure gradient.
We know the unit of pressure is N/m2N/{{m}^{2}} and that of distance is mm.
Therefore,
N/m2m=N/m3\dfrac{N/{{m}^{2}}}{m}=N/{{m}^{3}}
We can also write the same unit as Nm−3N{{m}^{-3}}

So, the correct answer is “Option D”.

Note: For solving this question, if we do not know the unit of pressure we can derive the same by using the basic definition of pressure that is force upon area. So, by knowing the basic dimensions and definitions of parameters we can derive the units of any physical quantity.