a multipath pipeline with two parallel branches around an obstruction Given flow in branch 1 (Q_1) = 0.2200 m^3/s; flow in branch 2 (Q_2) = 0.2250 m^3/s, determine the total flow (Q) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow in branch 1 (Q_1) = 0.2200 m^3/s, flow in branch 2 (Q_2) = 0.2250 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q = 0.4450\ \text{m^3/s}

6. Step 6 — Check: returning Q = 0.4450 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.8900 — kept a factor of two that cancels in the correct rearrangement.
• 0.2225 — dropped that same factor in the other direction.
• 0.4895 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

multipath pipeline problems in a looped water distribution network Given total flow (Q) = 0.3550 m^3/s; flow in branch 2 (Q_2) = 0.0350 m^3/s, determine the flow in branch 1 (Q_1) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q_1 is given, so isolate Q_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q_1 stands alone on the left-hand side.

3. Step 3

   $$List the givens: total flow (Q) = 0.3550 m^3/s, flow in branch 2 (Q_2) = 0.0350 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q_{1} = 0.3200\ \text{m^3/s}

6. Step 6 — Check: returning Q_1 = 0.3200 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.6400 — kept a factor of two that cancels in the correct rearrangement.
• 0.1600 — dropped that same factor in the other direction.
• 0.3520 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

a multipath pipeline delivering flow to two service pipes Given total flow (Q) = 0.1000 m^3/s; flow in branch 1 (Q_1) = 0.2900 m^3/s, determine the flow in branch 2 (Q_2) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q_2 is given, so isolate Q_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q_2 stands alone on the left-hand side.

3. Step 3

   $$List the givens: total flow (Q) = 0.1000 m^3/s, flow in branch 1 (Q_1) = 0.2900 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q_{2} = -0.1900\ \text{m^3/s}

6. Step 6 — Check: returning Q_2 = -0.1900 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -0.3800 — kept a factor of two that cancels in the correct rearrangement.
• -0.0950 — dropped that same factor in the other direction.
• -0.2090 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

a multipath pipeline with two parallel branches around an obstruction Given flow in branch 1 (Q_1) = 0.2150 m^3/s; flow in branch 2 (Q_2) = 0.0250 m^3/s, determine the total flow (Q) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow in branch 1 (Q_1) = 0.2150 m^3/s, flow in branch 2 (Q_2) = 0.0250 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q = 0.2400\ \text{m^3/s}

6. Step 6 — Check: returning Q = 0.2400 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.4800 — kept a factor of two that cancels in the correct rearrangement.
• 0.1200 — dropped that same factor in the other direction.
• 0.2640 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

multipath pipeline problems in a looped water distribution network Given total flow (Q) = 0.3250 m^3/s; flow in branch 2 (Q_2) = 0.1850 m^3/s, determine the flow in branch 1 (Q_1) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q_1 is given, so isolate Q_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q_1 stands alone on the left-hand side.

3. Step 3

   $$List the givens: total flow (Q) = 0.3250 m^3/s, flow in branch 2 (Q_2) = 0.1850 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q_{1} = 0.1400\ \text{m^3/s}

6. Step 6 — Check: returning Q_1 = 0.1400 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.2800 — kept a factor of two that cancels in the correct rearrangement.
• 0.0700 — dropped that same factor in the other direction.
• 0.1540 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

a multipath pipeline delivering flow to two service pipes Given total flow (Q) = 0.1300 m^3/s; flow in branch 1 (Q_1) = 0.2850 m^3/s, determine the flow in branch 2 (Q_2) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q_2 is given, so isolate Q_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q_2 stands alone on the left-hand side.

3. Step 3

   $$List the givens: total flow (Q) = 0.1300 m^3/s, flow in branch 1 (Q_1) = 0.2850 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q_{2} = -0.1550\ \text{m^3/s}

6. Step 6 — Check: returning Q_2 = -0.1550 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -0.3100 — kept a factor of two that cancels in the correct rearrangement.
• -0.0775 — dropped that same factor in the other direction.
• -0.1705 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

a multipath pipeline with two parallel branches around an obstruction Given flow in branch 1 (Q_1) = 0.2200 m^3/s; flow in branch 2 (Q_2) = 0.0750 m^3/s, determine the total flow (Q) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow in branch 1 (Q_1) = 0.2200 m^3/s, flow in branch 2 (Q_2) = 0.0750 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q = 0.2950\ \text{m^3/s}

6. Step 6 — Check: returning Q = 0.2950 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.5900 — kept a factor of two that cancels in the correct rearrangement.
• 0.1475 — dropped that same factor in the other direction.
• 0.3245 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

multipath pipeline problems in a looped water distribution network Given total flow (Q) = 0.5000 m^3/s; flow in branch 2 (Q_2) = 0.1700 m^3/s, determine the flow in branch 1 (Q_1) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q_1 is given, so isolate Q_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q_1 stands alone on the left-hand side.

3. Step 3

   $$List the givens: total flow (Q) = 0.5000 m^3/s, flow in branch 2 (Q_2) = 0.1700 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q_{1} = 0.3300\ \text{m^3/s}

6. Step 6 — Check: returning Q_1 = 0.3300 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.6600 — kept a factor of two that cancels in the correct rearrangement.
• 0.1650 — dropped that same factor in the other direction.
• 0.3630 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

a multipath pipeline delivering flow to two service pipes Given total flow (Q) = 0.0550 m^3/s; flow in branch 1 (Q_1) = 0.1300 m^3/s, determine the flow in branch 2 (Q_2) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q_2 is given, so isolate Q_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q_2 stands alone on the left-hand side.

3. Step 3

   $$List the givens: total flow (Q) = 0.0550 m^3/s, flow in branch 1 (Q_1) = 0.1300 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q_{2} = -0.0750\ \text{m^3/s}

6. Step 6 — Check: returning Q_2 = -0.0750 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -0.1500 — kept a factor of two that cancels in the correct rearrangement.
• -0.0375 — dropped that same factor in the other direction.
• -0.0825 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems

a multipath pipeline with two parallel branches around an obstruction Given flow in branch 1 (Q_1) = 0.2400 m^3/s; flow in branch 2 (Q_2) = 0.1150 m^3/s, determine the total flow (Q) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Multipath pipeline problems (continuity/head-loss balance).
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Multipath pipeline problems split total flow between parallel branches so head loss is equal in each path.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow in branch 1 (Q_1) = 0.2400 m^3/s, flow in branch 2 (Q_2) = 0.1150 m^3/s$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   Q = 0.3550\ \text{m^3/s}

6. Step 6 — Check: returning Q = 0.3550 m^3/s to

   $$Q = Q_1 + Q_2, \qquad h_{f,1} = h_{f,2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.7100 — kept a factor of two that cancels in the correct rearrangement.
• 0.1775 — dropped that same factor in the other direction.
• 0.3905 — rounded an intermediate value before the final step.

Reference: FE Handbook — Multipath Pipeline Problems