Ethanol is contained in a large tank under a pressure 3.1 bar absolute. When the valve on the bottom of the tank is opened, the ethanol drained freely through a 1cm ID tube those outlet is 7m below the surface of the ethanol.The pressure at the outlet of the discharge pipe is 1 atm.

a) Use the bernoulli equation to estimate the ethanol discharge velocity and the flow rate in L/min when the valve is fully opened. Neglect the rate of fall of the ethanol level in the tank.

b) When the dicharged valve is partially closed , the flow rate decreases, which means that delta U^2 /2 changes. however the other two terms in the bernoulli equation ( delta P/density and g delta z) remain the same. How do you account for this apparently contradictory result ?