Question

Air$(\rho =1.2kg/m^3$ and kinematic viscosity, $v=2\times {10}^{-5}{m}^2/s)$ with a velocity of 2 m/s flows over the top surface of a flat plate of length 2.5 m. If the average value of friction coefficient is $C_f=\frac{1.328}{{\sqrt{Re}}_x}$, the total drag force (in N) per unit width of the plate is_________

• A. 0.0159

Answer 1

The correct option is A 0.0159

Drag force = Average shear stress $\times$ area
where $\overline{\tau }$ = average shear stress

=$\overline{C_f}\times \frac{\rho U_{\infty }^2}{2}=\frac{1.328}{\sqrt{R{e}_L}}\times \frac{\rho U_{\infty }^2}{2}$

$R{e}_L$ = Local Reynold's number at trailing edge.

=$\frac{U_{\infty }L\rho }{\mu }=\frac{2\times 2.5\times 1.2}{1.2\times 2\times {10}^{-5}}$

=$2.5\times {10}^5$ (laminar flow)

Drag force: $F_D=\tau \times A$

$=\frac{1.328}{\sqrt{2.5\times {10}^5}}\times \frac{1.2\times 2^2}{2}\times (2.5\times 1)$

=0.0159 N