Question Number 132173 by I want to learn more last updated on 11/Feb/21
$$\mathrm{If}\:\:\:\:\mathrm{v}\:\:\:=\:\:\:\frac{\sqrt{\mathrm{p}\:\:\:+\:\:\:\frac{\mathrm{1}}{\mathrm{n}}}}{\mathrm{x}},\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\:\:\mathrm{p}\:\:=\:\:\:\mathrm{pressure}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\:\:\:\:\mathrm{n}\:\:\:\mathrm{and}\:\:\:\mathrm{x} \\ $$
Commented by mr W last updated on 12/Feb/21
![question is incomplete! if dimension of v is not given, you can′t determine dimension of x. assume v is velocity [v]=(m/s) [p]=(N/m^2 ) [n]=(1/([p]))=(m^2 /N) [x]=((√([p]))/([v]))=((√(N/m^2 ))/(m/s))=((s(√N))/m^2 )](https://www.tinkutara.com/question/Q132184.png)
$${question}\:{is}\:{incomplete}! \\ $$$${if}\:{dimension}\:{of}\:{v}\:{is}\:{not}\:{given},\:{you} \\ $$$${can}'{t}\:{determine}\:{dimension}\:{of}\:{x}. \\ $$$$ \\ $$$${assume}\:{v}\:{is}\:{velocity} \\ $$$$\left[{v}\right]=\frac{{m}}{{s}} \\ $$$$\left[{p}\right]=\frac{{N}}{{m}^{\mathrm{2}} } \\ $$$$\left[{n}\right]=\frac{\mathrm{1}}{\left[{p}\right]}=\frac{{m}^{\mathrm{2}} }{{N}} \\ $$$$\left[{x}\right]=\frac{\sqrt{\left[{p}\right]}}{\left[{v}\right]}=\frac{\sqrt{\frac{{N}}{{m}^{\mathrm{2}} }}}{\frac{{m}}{{s}}}=\frac{{s}\sqrt{{N}}}{{m}^{\mathrm{2}} } \\ $$
Commented by I want to learn more last updated on 12/Feb/21
$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{now}\:\mathrm{understand}.\:\mathrm{I}\:\mathrm{appreciate}. \\ $$