Question

Use dimensional analysis to check if expression P=1/2^Pv^2 +pgh is correct,given that,p is pressure in pascal,p is density in kgm^-3,v is velocity in m/s,g is acceleration due to gravity in m/s^2 and h is the height in m

Answer 1

We need to determine the dimensions of each part of equation:

$$dim⁡P=MT^{-2} L^{-1}$$

$$dim⁡[1/2 ρv^2 ] =dim⁡[1/2] dim⁡[ρ] dim⁡[v^2 ]=1(ML^{-3} ) (LT^{-1} )^2=MT^{-2} L^{-1}$$

$$dim⁡[ρgh] =dim⁡[ρ]dim⁡[g]dim⁡[h]=(ML^{-3} )(LT^{-2})(L)=MT^{-2} L^{-1}$$

We have the same result in each case, thus the expression is correct.