Question

What are the dimensions of pressure gradient?

MLT−2

ML−2T−2

ML3T−2

M−2L2T−3

Answer 1

Answer on Question #51851-Physics-Mechanics-Kinematics-Dynamics

What are the dimensions of pressure gradient?

MLT-2

ML-2T-2

ML3T-2

M-2L2T-3

Solution

Pressure has dimension of

$$[ p ] = \frac {N}{m ^ {2}}.$$

Which is

$$[ p ] = \frac {k g \cdot \frac {m}{s ^ {2}}}{m ^ {2}} = \frac {k g}{s ^ {2} \cdot m}.$$

Hence, pressure gradient will have dimension

$$[ \nabla p ] = [ \nabla ] \cdot [ p ] = \frac {1}{m} \cdot \frac {k g}{s ^ {2} \cdot m} = \frac {k g}{(s \cdot m) ^ {2}} = M L ^ {- 2} T ^ {- 2}.$$

Answer: $ML^{-2}T^{-2}$

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