HGL and EGL for pipes in series

Reservoir A (higher) feeds reservoir B through three pipes in series, with $d_1 < d_3 < d_2$. Both reservoir surfaces are at rest, so HGL and EGL start at the water surface of A and end at the water surface of B.

Rules used

• EGL falls in the direction of flow: slope $= f V^2/(2gd)$, so it is steepest in the smallest pipe 1 and flattest in pipe 2.
• HGL is below the EGL by $V^2/2g$; the gap is largest in pipe 1 (highest velocity) and smallest in pipe 2.
• Sudden drops of the EGL: entrance loss $0.5V_1^2/2g$; expansion from $d_1$ to $d_2$: $(V_1 - V_2)^2/2g$; contraction from $d_2$ to $d_3$: $0.5\left(1-\dfrac{A_3}{A_2}\right)V_3^2/2g$ (approximately); exit loss into B: $V_3^2/2g$.
• At the exit, the whole velocity head is lost, so the EGL falls to the surface of B and both lines end at the water level of B.

 A __                                           
    |\ entrance                 
    | \___ EGL                              
    |     `-.__ (steep, d1)                  
    |  HGL     `-.   | expansion drop        
    |  (gap     `-.__|`-.__ (flat, d2)     
    |   V1²/2g)         |  `-.__|contraction
    |                    HGL     |`-.__ (d3)
    |==[d1]=======[d2 big]=======[d3]=====> 
                                       exit drop
                                          \__ B

• The HGL rises after the expansion (velocity falls) and falls again after the contraction (velocity rises).
• Total of all drops (friction + minor losses) equals the difference of the two reservoir levels, $H = h_{f1} + h_{f2} + h_{f3} + h_{entry} + h_{exp} + h_{contr} + h_{exit}$.