WEEK $2$ PROBLEMS

For steady flow through a conical nozzle of length $L,$ the velocity in the direction of flow, $x$ direction, is approximately

$V_x=v_1(1+\frac{x}{L})$

where V$1$ is the velocity at the entrance of the nozzle. Determine the acceleration in the x direction.

$2.$ In micropipet systems that measure membrane and cortical tension, the pressure difference $p=Pp-$ Po is produced by a column of fluid. Thus, $p=gh.$ The fluid is water $(=1gc{m}^{-3}),$ and the minimum column height that can be maintained is $2\mathrm{.}5m.($

$($a$)$ Determine the minimum pressure that can be generated.

$($b$)$ For a cell of radius $6m$ and a micropipet radius of $1\mathrm{.}5m,$ determine the smallest cortical tension that can be measured.

$($The value of acceleration due to gravity is $980cm{s}^{-1}.)$

$p=2T_c(\frac{1}{R_p}+\frac{1}{R_c})$

For the following data, determine the type of fluid and the values of the properties characterizing the fluid.

$\backslash$table$[[$Shear Rate $(s^{-1}),$Shear Stress $)],[0\mathrm{.}1,0\mathrm{.}0002],[0\mathrm{.}5,0\mathrm{.}0019],[1\mathrm{.}0,0\mathrm{.}0049],[5\mathrm{.}0,0\mathrm{.}056],[10,0\mathrm{.}14],[50,1\mathrm{.}77],[{}_{yx}=z_x^{}$