Washburn equation for fluid flow in horizontal capillary is given by : $\frac{dL}{dt} = \frac{γR}{4µL}$
Find the time dependencies of length of travel, $L(T)$ and average velocity.
I can find the first part by integrating the Washburn eqn but I am a little confused as to how to find the average velocity as a function of t.
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$\begingroup$Remember that the average velocity is equal to $$\frac{\Delta L}{\Delta t}=\frac{L_2-L_1}{t_2-t_1}$$ Which can be found by integrating the velocity over a certain interval and dividing it by the length of that interval.
The expression $\frac{dL}{dt}$ is equal to the instantaneous velocity, so integrating the function gives $$L(t) = \sqrt{\frac{\gamma Rt}{2\mu}}$$
and so the average velocity from $t=a$ to $t=b$ is
$$\frac{L(b)-L(a)}{b-a} = \frac{\sqrt{\frac{\gamma Rb}{2\mu}}-\sqrt{\frac{\gamma Ra}{2\mu}}}{b-a} =\sqrt{\frac{\gamma R}{2\mu}}\frac{\sqrt{b}-\sqrt{a}}{b-a}$$
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