In finding Reynold’s number, the characteristic length of a circu
A. d
B. 2d
C. 5d
D. 10d
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Reynold Number:
\({R_e} = \frac{{\rho UL}}{\mu }\)
Where U is the average stream velocity and L is the characteristics length/width.
The hydraulic diameter which is used as the characteristic length in the determination of friction factor, instead of ordinary geometrical diameter, is defined as
\({D_h} = \frac{{4{A_w}}}{{{P_w}}}\)
where Aw is the flow area and Pw is the wetted perimeter
Circular pipe of diameter d:
\({D_h} = \frac{{4{A_w}}}{{{P_w}}} = \frac{{4 \times \frac{\pi }{4}{d^2}}}{{\pi d}} = d\)
The square duct of size a:
\({D_h} = \frac{{4{A_w}}}{{{P_w}}} = \frac{{4 \times {a^2}}}{{4a}} = a\)
The rectangular duct of size a × b:
\({D_h} = \frac{{4{A_w}}}{{{P_w}}} = \frac{{4 \times ab}}{{2\left( {a + b} \right)}} = \frac{{2ab}}{{a + b}}\)
