Question

A thin smooth plate 1 m wide and 2 m long is towed through water at a velocity of 2 m/s. Assuming that boundary remains laminar, then drag on both sides of the plate is (kinematic viscosity = ${10}^{-6}{m}^2/s$)

• A. 5.3 N
• B. 26.6 N
• C. 53 N
• D. 72.5 N

Answer 1

The correct option is A 5.3 N

Friction coefficient, $\overline{C}f=\frac{1.328}{\sqrt{R{e}_L}}R{e}_L=\frac{VL}{\nu }=\frac{2\times 2}{{10}^{-6}}=4\times {10}^6\therefore {\overline{C}}_f=\frac{1.328}{\sqrt{4\times {10}^6}}=6.64\times {10}^{-4}$
The drag force on both sides of the plate,
$F_D=2{\overline{C}}_f\left(\frac{1}{2}\rho V^2\right)\left(BL\right)=2\times 6.64\times {10}^{-4}\times \frac{1}{2}\times 1000\times \left(2^2\right)\times 1\times 2$
=5.31 N