$4\mathrm{.}5\mathrm{.}3.$ The valve in an oil pipeline must be closed rapidly when a leak is detected, but not so fast as to produce a large pressure

rise. A $1,250-$m$-$long pipeline carries oil $($S$.$ G$.=0\mathrm{.}85,$ bulk modulus of $1\mathrm{.}5{10}^9\frac{N}{m^2})$ through a $0\mathrm{.}5-$m$-$diameter steel pipe

with expansion joints and a wall thickness of $2\mathrm{.}5cm.$ The normal discharge rate is $1\mathrm{.}65\frac{m^3}{s}.$ Determine the minimum valve

closure time that would prevent a large pressure rise $($i$.$e$.,$ rapid closure$).$The solution is t$=2\mathrm{.}00$s