The original question is as shown below:
My Solution:
I solved this question and got $0.38 N$ for both sides of the plate but the correct answer as per the test is $\color{red}{ \;0.76 N}$ The only difference between the asnwers is that I used the formula of local drag coefficient $$C_f=\frac{0.664}{\sqrt{Re_x}}$$ $$F_D=2\cdot\frac12C_D\rho AU^2=0.00094(1000)(0.15\cdot3)(3^3)=0.38 N$$ and in the solution they used $$C_D=\frac{1.328}{\sqrt{Re_L}}$$
My Concern and Observation: Which formula should we use according to this question and in general sense also. I thought, when we consider full length of the object we use $C_D$ and when not full length then we use $C_f$ Maybe I am wrong, if so, please let me know when to use which equation??
Ok. The question is what keywords to look for to determine when to use $C_D$ vs. $C_f$. Generally, if there’s no reason not to, use $C_D$. That’s because using $C_D$ of a shape in the appropriate equation will return the frictional energy losses or pressure losses due to friction. If unspecified, use $C_D$. However, if the question mentions “one side of” or “calculate the drag/pressure drop on one side” the answer will probably use $C_f$. The best bet is to draw a diagram, and if fluid is flowing around the whole object, use $C_D$, and if fluid is flowing just on one side of the object, consider using $C_f$. So, in this case, because “one side” is not specified, you would use $C_D$.
I found a study guide which uses $C_f$ for local drag and $C_D$ for total drag on the object (a plate):
In my experience, $C_D$ generally means the total drag on an object, whether the object is a cylinder, sphere, plate, person, or any other object you can imagine.
So, $F_d =12ρ⋅U_∞^2⋅A⋅C_D$ (units of force, or mass $\times$ length $\times$ time$^-$ $^2$ e.g. newtons)
$C_D$ is found by integrating $C_{f_x}$ over the length of an object.