Poiseuille Flow: Consider a pressure-driven (gradient DeltaP/L = (P_in -P_out)/L

Question

Poiseuille Flow: Consider a pressure-driven (gradient DeltaP/L = (P_in -P_out)/L) flow of a fluid of viscosity mu in a tube of circular cross-section with radius R and length L. Starting from the NSE, show for fully-developed, steady flow, that the volumetric flow rate is:[10] Show that the magnitude of the shear stress T_rz at the wall is: Using your answer from parts (a) and (b), obtain an expression for the friction factor f in terms of the Reynolds number Re = D . v_z,av p/mu [5] Oil (viscosity 0.4 N-s/m^2) flows through a tube of 5 mm radius. Assuming fully-developed steady-state flow with a pressure gradient of 900. Pa/m, determine the volumetric flow rate and the shear stress at the tube wall. [5]

Explanation / Answer

here,

4.

magnitude of charges , q = 4.65 * 10^-10 C

electric field , E = 1660 N/C

let the distance between the charges be x

as both are equal in magnitude

electric feild , E = k * q / (0.5 * x)^2 + k * q / (0.5 * x)^2

2 * 4.65 * 10^-10 * 9 * 10^9 / ( 0.5 x)^2 = 1660

x = 0.14 m

distance between the charrges is 14 cm or 0.14 m

5.

for the charges of equal sign,

as the charges are equal

the magnitude of electric feild at the centre is zero

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