In a two-dimensional pipe with a width of 1m under atmospheric pressure as shown in the figure, flow occurs. The A-A cross-section is rectangular. At the inlet, flow enters at a uniform velocity of 30m/sec. The Venturi wall is expressed as = 2 + 2 2 (m) with the Venturi center axis. The length of the pipe in the axial direction is 3m.

1. What assumption should be made to use the Bernoulli equation to obtain the pressure distribution? 2. Calculate the mass flow rate and volume flow rate at the inlet. 3. Describe the location of the minimum pressure and the reason why, using the first derivative of y at the point where the cross-sectional area is the smallest. 4. Calculate the velocity and pressure at the point of minimum pressure. 5. If a U-shaped manometer is connected to the inlet and the point of minimum pressure to measure the pressure difference between them, and the manometer is filled with water (density: 998 kg/m3 and gravity acceleration: 9.8m/s2), what is the height difference between the two arms of the manometer? Assume that the effect of air density is negligible. 6. Calculate the force acting in the axial direction. Gravity acts in the y-direction.