In a steady flow, an incompressible fluid enters a rectangular channel at a uniform velocity $u_1=U.$ The height of the channel at the inlet is $H.$ The fluid exits at the outlet of height $3H$ at a non$-$uniform velocity whose profile is

$u_2=U_{\text{m}\text{a}\text{x}}cos(\frac{y}{3H})$

where $y$ is measured from the center of the channel. What is the relation between $U$ and $U_{\text{m}\text{a}\text{x}}.$