A dimensionally consistent relation for the v | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The volume flow rate $V$ (Poiseuille's Law) is given by the formula $V = \frac{\pi P r^4}{8 \eta l}$.To verify this dimensionally:Dimensions of $V

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The volume flow rate $V$ (Poiseuille's Law) is given by the formula $V = \frac{\pi P r^4}{8 \eta l}$.To verify this dimensionally:Dimensions of $V = [L^3 T^{-1}]$.Dimensions of $P = [M L^{-1} T^{-2}]$.Dimensions of $r = [L]$.Dimensions of $\eta = [M L^{-1} T^{-1}]$.Dimensions of $l = [L]$.Substituting these into the $RHS$: $\frac{[M L^{-1} T^{-2}] [L^4]}{[M L^{-1} T^{-1}] [L]} = \frac{[M L^3 T^{-2}]}{[M T^{-1}]} = [L^3 T^{-1}]$.Since the dimensions of $LHS$ and $RHS$ match,the correct relation is $V = \frac{\pi P r^4}{8 \eta l}$.

$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

Similar Questions

If the units of force,energy,and velocity are respectively $10\, N$,$100\, J$,and $5\, m/s$,then the units of length,mass,and time will be:

$A$ bomb explodes at time $t=0$ in a uniform,isotropic medium of density $\rho$ and releases energy $E$,generating a spherical blast wave. The radius $R$ of this blast wave varies with time $t$ as

$(P+\frac{a}{V^2})(V-b)=RT$ represents the equation of state of some gases. Where $P$ is the pressure,$V$ is the volume,$T$ is the temperature and $a, b, R$ are the constants. The physical quantity,which has the same dimensional formula as that of $\frac{b^2}{a}$,will be

If mass is written as $m=kc^{p} G^{-1 / 2} \,h^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $k$ a dimensionless constant)

If $x = at + bt^2$,where $x$ is the distance travelled by the body in kilometres while $t$ is the time in seconds,then the units of $b$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module