An inviscid incompressible liquid with density p flows in a wide conduit of height H and width B into the page as shown in Figure 1. The inlet stream travels at a uniform speed U and fills the conduit. The depth of the outlet stream is less than H. Air with negligible density fills the gap above the outlet stream. Gravity acts downward with acceleration g. Assume the flow is steady for the following items. (a) Denote the outlet stream depth and speed by h and u, respectively, and write down a set of equations that will allow U, u, and h to be determined in terms of p, H, and g hint: take into account the hydrostatic pressure of liquid]. (b) Solve for U, u, and h in termis of p, H, and g and show that h = H/2, u = VgH and U - VgH/2 (hint: solve for h first]. air Figure 1: Problem 1