Solving for y by ratio and proportion
$\dfrac{y}{D_7} = \dfrac{y + 6}{D_1}$
$D_1y = D_7(y + 6)$
$450y = 150(y + 6)$
$300y = 900$
$y = 3 \, \text{ m}$
Solving for diameters by ratio and proportion
$\dfrac{D_2}{5 + y} = \dfrac{D_3}{4 + y} = \dfrac{D_4}{3 + y} = \dfrac{D_5}{2 + y} = \dfrac{D_6}{1 + y} = \dfrac{D_7}{y}$
$\dfrac{D_2}{5 + 3} = \dfrac{D_3}{4 + 3} = \dfrac{D_4}{3 + 3} = \dfrac{D_5}{2 + 3} = \dfrac{D_6}{1 + 3} = \dfrac{150}{3}$
$\dfrac{D_2}{8} = \dfrac{D_3}{7} = \dfrac{D_4}{6} = \dfrac{D_5}{5} = \dfrac{D_6}{4} = 50$
$D_2 = 50(8) = 400 \, \text{ mm}$
$D_3 = 50(7) = 350 \, \text{ mm}$
$D_4 = 50(6) = 300 \, \text{ mm}$
$D_5 = 50(5) = 250 \, \text{ mm}$
$D_6 = 50(4) = 200 \, \text{ mm}$
Formula for velocity of flow
$Q = vA$
$v = Q/A$
Velocity at sections 1-m apart
$v_1 = 0.15 / [ \, \frac{1}{4} \pi (0.450^2) \, ] = 0.943 \, \text{ m/sec}$
$v_2 = 0.15 / [ \, \frac{1}{4} \pi (0.400^2) \, ] = 1.194 \, \text{ m/sec}$
$v_3 = 0.15 / [ \, \frac{1}{4} \pi (0.350^2) \, ] = 1.559 \, \text{ m/sec}$
$v_4 = 0.15 / [ \, \frac{1}{4} \pi (0.300^2) \, ] = 2.122 \, \text{ m/sec}$
$v_5 = 0.15 / [ \, \frac{1}{4} \pi (0.250^2) \, ] = 3.056 \, \text{ m/sec}$
$v_6 = 0.15 / [ \, \frac{1}{4} \pi (0.200^2) \, ] = 4.775 \, \text{ m/sec}$
$v_7 = 0.15 / [ \, \frac{1}{4} \pi (0.150^2) \, ] = 8.488 \, \text{ m/sec}$
Graph of velocity of flow versus length of pipe (plotted in MS Excel)
