Question

For the laminar flow of water over a sphere, the drag coefficient $C_F$ is defined as $C_F=F/\left(\rho U^2{D}^2\right)$, where F is the drag force, $\rho$ is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/$m^3$. When the diameter of the sphere is 100 mm and the fluid velocity is 2 m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200 mm under dynamically similar conditions, the drag force (in N) on this sphere is_______

• A. 20

Answer 1

The correct option is A 20
Drag coefficient,
$C_F=\frac{F}{\rho U^2{D}^2}$

or Drag force,
F=$C_F\rho U^2{D}^2$

Given data for sphere-1
${\rho }_1=1000kg/m^3$
$D_1=100mm=0.1m$
$U_1=2m/s$
$C_F=0.5$

For sphere-2
${\rho }_2=1000kg/m^3$
$D_2=200mm=0.2m$
For dynamically similar conditions,
$(Re{)}_1=(Re{)}_2$

$\frac{U_1{D}_1}{v_1}$=$\frac{U_2{D}_2}{v_2}$

or $U_1{D}_1$=$U_2{D}_2$

$2\times 0.1=U_2\times 0.2$
or $U_2=1m/s$

$F_2=C_F\rho U_2^2{D}_2^2$

$0.5\times 1000\times (1{)}^2\times (0.2{)}^2$
=20 N