Pipes of lengths $$l_1, l_2$$ etc and diameter $$d_1, d_2$$, etc are connectedin series. A single pipe of length $$l_1 + l_2 + l_3 + ....$$ having same pressure loss as all pipes in series will have diameter equal to

$$\left(\frac{l_1 + l_2 + l_3 + ....}{\frac{l_1}{d_1^4} + \frac{l_2}{d_2^4} + ......}\right)^{\frac{1}{4}}$$

$$\left(\frac{l_1 + l_2 + l_3 + ....}{\frac{l_1}{d_1^5} + \frac{l_2}{d_2^5} + ......}\right)^{\frac{1}{5}}$$

$$\left(\frac{l_1 + l_2 + l_3 + ....}{\frac{l_1}{d_1^3} + \frac{l_2}{d_2^3} + ......}\right)^{\frac{1}{3}}$$

$$\left(\frac{l_1 + l_2 + l_3 + ....}{\frac{l_1}{d_1^2} + \frac{l_2}{d_2^2} + ......}\right)^{\frac{1}{2}}$$