Friction Loss worksheet

1. Pressure drop: 0.719 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 1.481 in = 0.037617 m)

   $\frac{0.00069399}{0.00111139}$$=0.624435\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{0.624435\times 0.037617}{0.0000008}$$=\mathrm{29,362}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.00106334

   $f$$=0.026207$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.026207\times \frac{36.576}{0.037617}\times \frac{{0.624435}^2}{2\times 9.80665}$$=0.506578\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 0.506578}{\mathrm{6,894.757293}}$$=0.719226\text{\hspace{0.17em}psi}$

2. Pressure drop: 298.878 psi

1. Find the head lost in each 100 ft of pipe with Hazen–Williams: 0.2083 × (100 ÷ C)^1.852 × Q^1.852 ÷ d^4.8655. Here C = 140 and the bore is 0.43 in

   $\frac{0.2083\times {\left(\frac{100}{140}\right)}^{1.852}\times {11}^{1.852}}{{0.43}^{4.8655}}$$=575.544132\text{\hspace{0.17em}ft per 100 ft}$

2. Scale that up to the full length of the run

   $575.544132\times \frac{120}{100}$$=690.652958\text{\hspace{0.17em}ft}$

3. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 210.511022}{\mathrm{6,894.757293}}$$=298.878102\text{\hspace{0.17em}psi}$

3. Pressure drop: 0.717 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 1.264 in = 0.032106 m)

   $\frac{0.00056781}{0.00080956}$$=0.701379\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{0.701379\times 0.032106}{0.0000011}$$=\mathrm{20,471}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.00124589

   $f$$=0.028296$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.028296\times \frac{22.86}{0.032106}\times \frac{{0.701379}^2}{2\times 9.80665}$$=0.505333\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 0.505333}{\mathrm{6,894.757293}}$$=0.717459\text{\hspace{0.17em}psi}$

4. Pressure drop: 211.536 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 0.584 in = 0.014834 m)

   $\frac{0.00088326}{0.00017282}$$=5.111012\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{5.111012\times 0.014834}{0.0000012}$$=\mathrm{63,179}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.01752777

   $f$$=0.046933$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.046933\times \frac{35.3568}{0.014834}\times \frac{{5.111012}^2}{2\times 9.80665}$$=148.992852\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 148.992852}{\mathrm{6,894.757293}}$$=211.536197\text{\hspace{0.17em}psi}$

5. Pressure drop: 34.618 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 0.722 in = 0.018339 m)

   $\frac{0.00075708}{0.00026414}$$=2.866232\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{2.866232\times 0.018339}{0.000001075}$$=\mathrm{48,896}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.01417759

   $f$$=0.04378$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.04378\times \frac{24.384}{0.018339}\times \frac{{2.866232}^2}{2\times 9.80665}$$=24.382533\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 24.382533}{\mathrm{6,894.757293}}$$=34.61769\text{\hspace{0.17em}psi}$

6. Pressure drop: 2.273 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 1.049 in = 0.026645 m)

   $\frac{0.0006309}{0.00055758}$$=1.131497\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{1.131497\times 0.026645}{0.00000065}$$=\mathrm{46,382}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.0000563

   $f$$=0.02144$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.02144\times \frac{30.48}{0.026645}\times \frac{{1.131497}^2}{2\times 9.80665}$$=1.600961\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 1.600961}{\mathrm{6,894.757293}}$$=2.273004\text{\hspace{0.17em}psi}$

7. Pressure drop: 0.584 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 1.481 in = 0.037617 m)

   $\frac{0.00056781}{0.00111139}$$=0.510901\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{0.510901\times 0.037617}{0.000001}$$=\mathrm{19,219}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.00398752

   $f$$=0.033156$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.033156\times \frac{35.052}{0.037617}\times \frac{{0.510901}^2}{2\times 9.80665}$$=0.411153\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 0.411153}{\mathrm{6,894.757293}}$$=0.583744\text{\hspace{0.17em}psi}$

8. Pressure drop: 17.562 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 0.745 in = 0.018923 m)

   $\frac{0.00069399}{0.00028124}$$=2.467656\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{2.467656\times 0.018923}{0.000001}$$=\mathrm{46,695}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.00317074

   $f$$=0.0291$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.0291\times \frac{25.908}{0.018923}\times \frac{{2.467656}^2}{2\times 9.80665}$$=12.369616\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 12.369616}{\mathrm{6,894.757293}}$$=17.562061\text{\hspace{0.17em}psi}$

9. Pressure drop: 13.367 psi

1. Find the head lost in each 100 ft of pipe with Hazen–Williams: 0.2083 × (100 ÷ C)^1.852 × Q^1.852 ÷ d^4.8655. Here C = 120 and the bore is 0.785 in

   $\frac{0.2083\times {\left(\frac{100}{120}\right)}^{1.852}\times {10}^{1.852}}{{0.785}^{4.8655}}$$=34.320791\text{\hspace{0.17em}ft per 100 ft}$

2. Scale that up to the full length of the run

   $34.320791\times \frac{90}{100}$$=30.888712\text{\hspace{0.17em}ft}$

3. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 9.414879}{\mathrm{6,894.757293}}$$=13.367002\text{\hspace{0.17em}psi}$

10. Pressure drop: 2.039 psi

1. Find how fast the water moves: divide the flow by the pipe's inside area (bore 1.069 in = 0.027153 m)

   $\frac{0.0006309}{0.00057905}$$=1.089555\text{\hspace{0.17em}m/s}$

2. Find the Reynolds number, Re = V × d ÷ ν. It shows whether the flow is smooth or swirling

   $\mathrm{Re}$$=\frac{1.089555\times 0.027153}{0.00000075}$$=\mathrm{39,446}$

3. Find the friction factor f from the Colebrook–White equation. It uses the roughness compared with the bore, ε ÷ d = 0.0016573

   $f$$=0.026421$

4. Find the head lost over the run with Darcy–Weisbach: h = f × (L ÷ d) × V² ÷ (2g)

   $h$$=0.026421\times \frac{24.384}{0.027153}\times \frac{{1.089555}^2}{2\times 9.80665}$$=1.436143\text{\hspace{0.17em}m}$

5. Turn head into pressure using the weight of water: ρ g h (water at 20 °C), in psi (about 0.4328 psi per foot of head)

   $\frac{998.2\times 9.80665\times 1.436143}{\mathrm{6,894.757293}}$$=2.038999\text{\hspace{0.17em}psi}$