If the force $F$ needed to move the wire in the given Fig. is $3.4 \times 10^{-3} \mathrm{~N}$, calculate the surface tension $~\gamma~$ of the enclosed fluid. Assume $~\ell=0.070 \mathrm{~m}$.

Poiseuille's equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, $R e$, exceeds approximately $2000.$ $R e$ is defined as

$$R e=\frac{2 \bar{v} r \rho}{\eta},$$

where $\bar{v}$ is the average speed of the fluid, $\rho$ is its density, $\eta$ is its viscosity, and $r$ is the radius of the tube in which the fluid is flowing. During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

Poiseuille's equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, $R e$, exceeds approximately $2000.$ $R e$ is defined as

$$R e=\frac{2 \bar{v} r \rho}{\eta},$$

where $\bar{v}$ is the average speed of the fluid, $\rho$ is its density, $\eta$ is its viscosity, and $r$ is the radius of the tube in which the fluid is flowing. Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta $(r=0.80 \mathrm{~cm})$ during the resting part of the heart's cycle is about $35 \mathrm{~cm} / \mathrm{s}$.

What must be the pressure difference between the two ends of a $1.9$-$\mathrm{km}$ section of pipe, $29 \mathrm{~cm}$ in diameter, if it is to transport oil $\left(\rho=950 \mathrm{~kg} / \mathrm{m}^3, \eta=0.20 \mathrm{~Pa} \cdot \mathrm{s}\right)$ at a rate of $650 \mathrm{~cm}^3 / \mathrm{s} ?$

What diameter must a $15.5$-$\mathrm{m}$-long air duct have if the ventilation and heating system is to replenish the air in a room $8.0 \mathrm{~m} \times 14.0 \mathrm{~m} \times 4.0 \mathrm{~m}$ every $12.0 \mathrm{~min}$ ? Assume the pump can exert a gauge pressure of $0.710 \times 10^{-3}\,\text{atm}$.

A gardener feels it is taking him too long to water a garden with a $\frac{3}{8}$-in.-diameter hose. By what factor will his time be cut if he uses a $\frac{5}{8}$-in.-diameter hose? Assume nothing else is changed.