Water flows through the pipe in the figure below and exits to the atmosphere at the right end of section C. The diameter of the pipe is 2.12 cm at A, 4.24 cm at B, and 0.880 cm at C. The gauge pressure in the pipe at the center of section A is 1.25 atm and the flow rate is 0.856 L/s. The vertical pipes are open to the air. Find the level (above the flow midline as shown) of the liquid-air interfaces in the two vertical pipes. Assume laminar nonviscous flow.
Use the definition of the volume flow rate in a pipe to find the speed of the water at point A and the relationship between the gauge pressures at points A and C to determine the level of the liquid-air interface at A. Use the continuity equation to express the speed of the water at B in terms of its speed at A and Bernoulli's equation for constant elevation to find the gauge pressure at B.