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1.Units, Dimensions and Measurement
medium

$r$ ત્રિજયા અને $l$ લંબાઇ ધરાવતી નળીમાં દબાણનો તફાવત $p$ રાખવાથી દર સેકન્ડે બહાર આવતા પ્રવાહીનું કદ $V$

A

$V = \frac{{\pi p{r^4}}}{{8\eta l}}$

B

$V = \frac{{\pi \eta l}}{{8p{r^4}}}$

C

$V = \frac{{8p\eta l}}{{\pi {r^4}}}$

D

$V = \frac{{\pi p\eta }}{{8l{r^4}}}$

Solution

$V$ = Rate of flow $=\frac{{{\rm{Volume }}}}{{{\rm{sec}}}} = [{L^3}{T^{ – 1}}]$,

$P$ = Pressure = $[M{L^{ – 1}}{T^{ – 2}}]$,

$r$ = Radius = $[L]$

$\eta $ = Coefficient of viscosity = $[M{L^{ – 1}}{T^{ – 1}}]$,

$ l$ = Length = $ [L]$

$V = \frac{{\pi P\,{r^4}}}{{8\eta l}}$

$\therefore [{L^3}{T^{ – 1}}] = \frac{{[M{L^{ – 1}}{T^{ – 2}}]\,[{L^4}]}}{{[M{L^{ – 1}}{T^{ – 1}}]\,[L]}}$ = $[{L^3}{T^{ – 1}}]$

$L.H.S. = R.H.S.$

Standard 11
Physics

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