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Figure $6\mathrm{.}6$: The two reservoirs connected by a smooth pipe.

Determine the difference between the levels in the two reservoirs shown in Figure $6\mathrm{.}6$ con$-$

nected by a smooth pipe, knowing that the downstream reservoir discharges water through

a sharp$-$edge weir with width $b=0\mathrm{.}5m$ under a head $H=0\mathrm{.}09m.$ Assume that there are no

losses at the entrance of the pipe. The weir measures the flow rate according to:

$Q=0\mathrm{.}41bH\sqrt[\phantom{2}]{2gH}$

Note: you will see more details on weirs in the part of the unit dedicated to open channel

flow. The diameter $D$ of the pipe is $0\mathrm{.}1m,$ and the length $L$ is $11\mathrm{.}4m.$ The viscosity

$u$ is

$0\mathrm{.}84*{10}^{-6}{m}^2{s}^{-1}.$

Hint: calculate $Q$ using the weir $($this is the same $Q$ flowing in the pipe because the system

is in steady state condition$).$ Calculate $Re$ and then calculate the friction coefficient $f$ or

read its value from the Moody diagram. Use $f$ to calculate $S_L$ and then you will be able

to calculate the difference between the two levels using the energy balance between the two

ends of the pipe.