- #36
gneill
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Rethinking it a bit, a simpler approach would be to let M be the total original mass of the tank plus water. You want to move a quantity m of that total mass (representing the water) through the pipe. Then
##(M - dm)dR = dm\;dr ~~~~## and as before, ##~~dr = L - dR##
##dR = L \frac{dm}{M}##
Integration is trivial, with limits 0 → m
##R = \frac{m}{M}L ##
##(M - dm)dR = dm\;dr ~~~~## and as before, ##~~dr = L - dR##
##dR = L \frac{dm}{M}##
Integration is trivial, with limits 0 → m
##R = \frac{m}{M}L ##