A valve is provided at the end of a cast iron pipe of diameter 150 mm and of thickness 10 mm. The water is flowing through the pipe, which is suddenly stopped by closing the valve. Determine the maximum velocity of waters, when the rise of pressure due to sudden closure of valve is 196.2 N/cm2. Take K for water as 19.62 x 104 N/cm2 and E for cast iron pipe as 11.772 x 106 N/cm2.

Given Data: $$ \begin{array}{l} D=150 \mathrm{~mm}=0.15 \mathrm{~m} \\ K=19.62 \times 10^{4} \mathrm{~N} / \mathrm{cm}^{2}=(19.62 \times 10^{8} )\mathrm{~N} / \mathrm{m}^{2} \\ E=11.772 \times 10^{6} \mathrm{~N} / \mathrm{cm}^{2}=(11.772 \times 10^{10} )\mathrm{~N} / \mathrm{m}^{2} \\ P=196.2 \mathrm{~N} / \mathrm{cm}^{2}=196.2 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2} \end{array} $$ From Relation, $p=v \sqrt{\frac{\rho}{\left(\frac{1}{k}+\frac{D}{E t}\right)}}$ $196.2 \times 10^{4}=V \times \sqrt{\frac{10^3}{\left(\frac{1}{19.62 \times 10^{8}}+\frac{0.15}{11.772 \times 10^{10} \times 0.01}\right)}}$ $V=1.57 \mathrm{~m} / \mathrm{s}$