Flow over a large field $($without any obstacles$)$ develops to take on a velocity profile described by

$v(z)=v_0(1-e^{\frac{-z}{}})$

Here $z$ is the vertical distance from the ground, $v_0$ is the velocity at large heights where the fluid does not feel the effects of the ground, and $$ is a length scale that contains information about regarding how high the effects of the ground are prevalent. Calculate the mass flow rate of the air through surface oriented perpendicular to the flow, starting from the ground and rising to a height of $15$ m $,$ and has a width of $1$ m $.$ Assume that $v_0=12\frac{m}{s}$ and $=5m.(8$ points$)$

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