Pipes of length l1, l2 etc and diameters d1, d2, etc. are connected in series. A single pipe of length l1 + l2 + l3 + …. having same pressure loss as all pipes in series will have diameter equal to

• A. \({\left( {\frac{{{l_1} + {l_2} + {l_3} + \ldots }}{{\frac{{{l_1}}}{{d_1^4}} + \frac{{{l_2}}}{{d_2^4}} + \ldots }}} \right)^{\frac{1}{4}}}\)
• B. \({\left( {\frac{{{l_1} + {l_2} + {l_3} + \ldots }}{{\frac{{{l_1}}}{{d_1^5}} + \frac{{{l_2}}}{{d_2^5}} + \ldots }}} \right)^{\frac{1}{5}}}\)
• C. \({\left( {\frac{{{l_1} + {l_2} + {l_3} + \ldots }}{{\frac{{{l_1}}}{{d_1^3}} + \frac{{{l_2}}}{{d_2^3}} + \ldots }}} \right)^{\frac{1}{3}}}\)
• D. \({\left( {\frac{{{l_1} + {l_2} + {l_3} + \ldots }}{{\frac{{{l_1}}}{{d_1^2}} + \frac{{{l_2}}}{{d_2^2}} + \ldots }}} \right)^{\frac{1}{2}}}\)