A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.7900; rainfall intensity (i) = 5.8000 in/hr; drainage area (A) = 46.0000 acre, determine the peak discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.7900, rainfall intensity (i) = 5.8000 in/hr, drainage area (A) = 46.0000 acre.

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

5. Step 5 — Evaluate:

   $$Q = 210.8\ \text{cfs}$$

6. Step 6 — Check: returning Q = 210.8 cfs to

   $$Q = C i A$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given rainfall intensity (i) = 1.8000 in/hr; drainage area (A) = 146.0 acre; peak discharge (Q) = 788.7 cfs, determine the runoff coefficient (C).

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except C is given, so isolate C 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: rainfall intensity (i) = 1.8000 in/hr, drainage area (A) = 146.0 acre, peak discharge (Q) = 788.7 cfs.

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

5. Step 5 — Evaluate:

   $$C = 3.0011$$

6. Step 6 — Check: returning C = 3.0011 to

   $$Q = C i A$$

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

Why the other options are there

• 6.0023 — kept a factor of two that cancels in the correct rearrangement.
• 1.5006 — dropped that same factor in the other direction.
• 3.3013 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.3800; drainage area (A) = 94.0000 acre; peak discharge (Q) = 175.2 cfs, determine the rainfall intensity (i) in in/hr.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except i is given, so isolate i 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.3800, drainage area (A) = 94.0000 acre, peak discharge (Q) = 175.2 cfs.

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

5. Step 5 — Evaluate:

   $$i = 4.9048\ \text{in/hr}$$

6. Step 6 — Check: returning i = 4.9048 in/hr to

   $$Q = C i A$$

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

Why the other options are there

• 9.8096 — kept a factor of two that cancels in the correct rearrangement.
• 2.4524 — dropped that same factor in the other direction.
• 5.3953 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.4000; rainfall intensity (i) = 3.9000 in/hr; peak discharge (Q) = 986.4 cfs, determine the drainage area (A) in acre.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except A is given, so isolate A 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.4000, rainfall intensity (i) = 3.9000 in/hr, peak discharge (Q) = 986.4 cfs.

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

5. Step 5 — Evaluate:

   $$A = 632.3\ \text{acre}$$

6. Step 6 — Check: returning A = 632.3 acre to

   $$Q = C i A$$

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

Why the other options are there

• 1,265 — kept a factor of two that cancels in the correct rearrangement.
• 316.2 — dropped that same factor in the other direction.
• 695.5 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.8100; rainfall intensity (i) = 4.3000 in/hr; drainage area (A) = 51.0000 acre, determine the peak discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.8100, rainfall intensity (i) = 4.3000 in/hr, drainage area (A) = 51.0000 acre.

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

5. Step 5 — Evaluate:

   $$Q = 177.6\ \text{cfs}$$

6. Step 6 — Check: returning Q = 177.6 cfs to

   $$Q = C i A$$

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

Why the other options are there

• 355.3 — kept a factor of two that cancels in the correct rearrangement.
• 88.8165 — dropped that same factor in the other direction.
• 195.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given rainfall intensity (i) = 2.0000 in/hr; drainage area (A) = 74.0000 acre; peak discharge (Q) = 112.9 cfs, determine the runoff coefficient (C).

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except C is given, so isolate C 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: rainfall intensity (i) = 2.0000 in/hr, drainage area (A) = 74.0000 acre, peak discharge (Q) = 112.9 cfs.

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

5. Step 5 — Evaluate:

   $$C = 0.7628$$

6. Step 6 — Check: returning C = 0.7628 to

   $$Q = C i A$$

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

Why the other options are there

• 1.5257 — kept a factor of two that cancels in the correct rearrangement.
• 0.3814 — dropped that same factor in the other direction.
• 0.8391 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.8200; drainage area (A) = 82.0000 acre; peak discharge (Q) = 252.2 cfs, determine the rainfall intensity (i) in in/hr.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except i is given, so isolate i 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.8200, drainage area (A) = 82.0000 acre, peak discharge (Q) = 252.2 cfs.

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

5. Step 5 — Evaluate:

   $$i = 3.7507\ \text{in/hr}$$

6. Step 6 — Check: returning i = 3.7507 in/hr to

   $$Q = C i A$$

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

Why the other options are there

• 7.5015 — kept a factor of two that cancels in the correct rearrangement.
• 1.8754 — dropped that same factor in the other direction.
• 4.1258 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.7200; rainfall intensity (i) = 1.5000 in/hr; peak discharge (Q) = 290.4 cfs, determine the drainage area (A) in acre.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except A is given, so isolate A 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.7200, rainfall intensity (i) = 1.5000 in/hr, peak discharge (Q) = 290.4 cfs.

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

5. Step 5 — Evaluate:

   $$A = 268.9\ \text{acre}$$

6. Step 6 — Check: returning A = 268.9 acre to

   $$Q = C i A$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.4400; rainfall intensity (i) = 1.9000 in/hr; drainage area (A) = 27.0000 acre, determine the peak discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: runoff coefficient (C) = 0.4400, rainfall intensity (i) = 1.9000 in/hr, drainage area (A) = 27.0000 acre.

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

5. Step 5 — Evaluate:

   $$Q = 22.5720\ \text{cfs}$$

6. Step 6 — Check: returning Q = 22.5720 cfs to

   $$Q = C i A$$

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

Why the other options are there

• 45.1440 — kept a factor of two that cancels in the correct rearrangement.
• 11.2860 — dropped that same factor in the other direction.
• 24.8292 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff

A hydrology and water resources problem uses Rational method. Given rainfall intensity (i) = 4.5000 in/hr; drainage area (A) = 119.0 acre; peak discharge (Q) = 164.5 cfs, determine the runoff coefficient (C).

Start with the thinking

• The governing relation printed in this handbook section is Rational method.
• Everything except C is given, so isolate C 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.
• Hydrology and Water Resources items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C i A$$

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

3. Step 3 — List the givens: rainfall intensity (i) = 4.5000 in/hr, drainage area (A) = 119.0 acre, peak discharge (Q) = 164.5 cfs.

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

5. Step 5 — Evaluate:

   $$C = 0.3072$$

6. Step 6 — Check: returning C = 0.3072 to

   $$Q = C i A$$

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

Why the other options are there

• 0.6144 — kept a factor of two that cancels in the correct rearrangement.
• 0.1536 — dropped that same factor in the other direction.
• 0.3379 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → NRCS (SCS) Rainfall-Runoff