Consider an increase of $1 \%$ in each of the radius of the artery, the viscosity of blood, and the density of blood, respectively. The percentage change in the flow rate of blood in the artery is (in $\%$)

What is turbulent flow? Give an example of turbulent flow.

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:

$(a)$ What is the largest average velocity of blood flow in an artery of radius $2 \times 10^{-3} \; m$ if the flow must remain laminar?
$(b)$ What is the corresponding flow rate? (Take viscosity of blood to be $2.084 \times 10^{-3} \; Pa \; s$).

$A$ highly viscous liquid of viscosity coefficient $\eta$ flows through a fixed horizontal cylindrical tube (fixed from the outer surface) of internal radius $r$,thickness $t$ $(t \ll r)$,and length $l$. The volume of liquid flowing per second is $Q$ and the pressure difference across the tube is $P$. If the modulus of rigidity of the material of the tube is $\beta$,the shear strain in the tube will be:

If it takes $5\,minutes$ to fill a $15\,litre$ bucket from a water tap of diameter $\frac{2}{\sqrt{\pi}}\,cm$,then the Reynolds number for the flow is (density of water $= 10^3\,kg/m^3$ and viscosity of water $= 10^{-3}\,Pa\cdot s$) close to