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 $l$ and having a pressure difference $p$ across its end, is
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 $l$ and having a pressure difference $p$ across its end, is
- 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
$V = \frac{{\pi p\eta }}{{8l{r^4}}}$
Similar Questions
Which of the following combinations has the dimension of electrical resistance ( ${ \varepsilon _0}$ is the permittivity of vacuum and ${\mu _0}$ is the permeability of vacuum) ?
Which of the following combinations has the dimension of electrical resistance ( ${ \varepsilon _0}$ is the permittivity of vacuum and ${\mu _0}$ is the permeability of vacuum) ?
- [JEE MAIN 2019]
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 / and having a pressure difference $P$ across its ends, is
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 / and having a pressure difference $P$ across its ends, is
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
- [AIIMS 2017]
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
- [JEE MAIN 2023]
Which one has the dimensions different from the remaining three
Which one has the dimensions different from the remaining three