Question $4($Bernoulli$)$

Methanol is contained in a large tank under a pressure of $3\mathrm{.}1$ bar absolute$.$ When a valve on the bottom of the tank is opened, the methanol drains freely though a $1-$cm ID tube whose outlet is $7\mathrm{.}00m$ below the surface of the methanol. The pressure at the outlet of the discharge pipe is $1$atm.

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

$($b$)$ When the discharge valve is partially closed, the flow rate decreases, which means that $\frac{u^2}{2}$ changes. However, the other two terms in the Bernoulli equation and $gz$ remain the same. How do you account for this apparently contradictory result? $($Hint: Examine the assumptions made in the derivation of the Bernoulli equation.$)$

$6$