Quantify the volume flow rate ?V/?t which passes through a single pore in the ba

Question

Quantify the volume flow rate ?V/?t which passes through a single pore in the basement membrane in the kidneys, using for the pressure difference across the membrane the value ?p = 0.99 kPa and a viscosity coefficient of ? = 1.41 x 10-3 Ns/m2. Use for the thickness of the basement membrane 48 nm and for the diameter of the pore, 13 nm.
Express the result in the unit [m3/s] and to three significant figures. If you must use scientific notation, please enter as follows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values, no units. For negative numbers, leave no space between the negative sign and the number: e.g. right: -1.00, wrong: - 1.00.

Explanation / Answer

Given pressure difference across the menbrane P = 0.99 kPa Coefficient of viscosity   = 1.41*10-3 Ns / m 2 Diamater of pore   D = 13 nm Radius of pore   R = 6.5 nm Thick ness of base memebrane   L = 48 *10-9 m Poiseuille's equation for viscous flow through a tube of radius R and length L              Q = v avg A                     = ( R2 P / 8 L ) A                   = R4 P   / 8 L                    = ( 6.5*10-9 m)4 ( 0.99*103 Pa ) / 8 (1.41*10-3 ) ( 48*10-9 m )                    = 1.03*10-20 m3 / s          

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