Which of the following quantities has the dimensions of $\frac{\pi P r^4}{8 Q l}$? (Where $P =$ pressure,$r =$ radius,$Q =$ volume flow rate in $m^3/s$,and $l =$ length.)

Water flows from a tap of diameter $1.5 \ cm$ with a flow rate of $7.5 \times 10^{-5} \ m^3 \ s^{-1}$. The coefficient of viscosity of water is $10^{-3} \ Pa \cdot s$. The flow is:

Water is conveyed through a uniform tube of $8 \text{ cm}$ in diameter and $3140 \text{ m}$ in length at the rate of $2 \times 10^{-3} \text{ m}^3/\text{s}$. The pressure required to maintain the flow is (Viscosity of water $= 10^{-3} \text{ SI units}$):

Two capillary tubes of the same length but different radii $r_1$ and $r_2$ are fitted in parallel to the bottom of a vessel. The pressure head is $P$. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is the same as before?

Under a constant pressure head,the rate of flow of liquid through a capillary tube is $V$. If the length of the capillary is doubled and the diameter of the bore is halved,the rate of flow would become

What is critical velocity? Write its equation.