(Solved): Water flows through the pipe contraction shown in the figure below. The tube connecting point 1 an ...

Water flows through the pipe contraction shown in the figure below. The tube connecting point 1 and point 2 is the periscope tube we seen in the lecture. The upper liquid surfaces inside the two tubes are both exposed to the atmosphere of \( P_{a t m} \). Let the vertical distance between point 3 and the free surface above it be \( x \). For the given 0.2-m difference in the manometer level, determine the volumetric flowrate, \( Q \), as a function of the diameter of the small pipe, \( D \). Your final expression should NOT have \( x \) in it. hint: - Find the pressure at point 2 in terms of \( x, P_{a t m} \), and all the other necessary quantities. - Find the pressure at point 4 similar to step a). - Find the pressure at point 3 following the generalized Bernoulli equation as discussed in this Wednesday's lecture. Notice that the flow rate \( Q \) is a function of the fluid speed at point \( 3 . \) Also notice that you cannot use the hydrostatic equation directly for point 3 . - Connect point 3 and point 2 through a streamline. This eventually allows you to find the relation between \( Q \) and \( D \), while \( x \) gets cancelled out during the simplification.