GATE2017 ME-2: 41

For the laminar flow of water over a sphere, the drag coefficient $C_{F}$ is defined as $C_{F}=F/(\rho U^{2} D^{2})$, 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 ________.

recategorized

Related questions

A $60$ mm-diameter water jet strikes a plate containing a hole of $40$ mm diameter as shown in the figure. Part of the jet passes through the hole horizontally and the remaining is deflected vertically. The density of water is $1000 kg/m^{3}$. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________.
The arrangement shown in the figure measures the velocity $V$ of a gas of density $1 kg/m^{3}$ flowing through a pipe. The acceleration due to gravity is $9.81 m/s^{2}$. If the manometric fluid is water (density $1000 \: kg/m^{3}$) and the velocity $V$ is $20 m/s$, the differential head $h$ (in mm) between the two arms of the manometer is __________.
Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by $\tau _{w}$. The axial positions $x_{1}$ and $x_{2}$ on the plate are measured from the leading edge in the direction of flow. If $x_{2} > x_{1}$ ... $\tau _{w}\mid _{x_{1}} < \tau _{w}\mid _{x_{2}}$
For a fully developed laminar flow of water (dynamic viscosity $0.001$ $P_{a-s}$) through a pipe of radius $5$ $cm$, the axial pressure gradient is −$10$ $Pa/m$. The magnitude of axial velocity (in $m/s$) at a radial location of $0.2$ $cm$ is _______