A 14 ha site is 6 ha pavement (C = 0.90) and 8 ha lawn (C = 0.20). The 10-year intensity for t_c = 15 min is 95 mm/h. Find the peak flow.

Start with the thinking

• Area-weight C before applying the formula.
• In SI, Q = CiA/360 with i in mm/h and A in hectares.

Step-by-step solution

1. Weighted runoff coefficient

   $$C = [0.90(6) + 0.20(8)]/14 = (5.40 + 1.60)/14$$

2. Evaluate

   $$C = 0.500$$

3. Rational formula

   $$Q = CiA/360$$

4. Substitute

   $$Q = 0.500(95)(14)/360 = 665/360$$

5. Result

   $$Q_p = 1.85 m^{3}/s$$

Why the other options are there

• 3.33 m³/s (C = 0.90 applied to the whole site)
• 0.74 m³/s (C = 0.20 applied to the whole site)

Reference: FE Reference Handbook — Hydrology — Rational method

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.8800; rainfall intensity (i) = 4.5000 in/hr; drainage area (A) = 88.0000 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) = 0.8800, rainfall intensity (i) = 4.5000 in/hr, drainage area (A) = 88.0000 acre.

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

5. Step 5 — Evaluate:

   $$Q = 348.5\ \text{cfs}$$

6. Step 6 — Check: returning Q = 348.5 cfs to

   $$Q = C i A$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given rainfall intensity (i) = 2.2000 in/hr; drainage area (A) = 67.0000 acre; peak discharge (Q) = 232.5 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) = 2.2000 in/hr, drainage area (A) = 67.0000 acre, peak discharge (Q) = 232.5 cfs.

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

5. Step 5 — Evaluate:

   $$C = 1.5773$$

6. Step 6 — Check: returning C = 1.5773 to

   $$Q = C i A$$

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

Why the other options are there

• 3.1547 — kept a factor of two that cancels in the correct rearrangement.
• 0.7887 — dropped that same factor in the other direction.
• 1.7351 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.9300; drainage area (A) = 50.0000 acre; peak discharge (Q) = 755.3 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) = 0.9300, drainage area (A) = 50.0000 acre, peak discharge (Q) = 755.3 cfs.

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

5. Step 5 — Evaluate:

   $$i = 16.2430\ \text{in/hr}$$

6. Step 6 — Check: returning i = 16.2430 in/hr to

   $$Q = C i A$$

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

Why the other options are there

• 32.4860 — kept a factor of two that cancels in the correct rearrangement.
• 8.1215 — dropped that same factor in the other direction.
• 17.8673 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.8800; rainfall intensity (i) = 5.7000 in/hr; peak discharge (Q) = 543.7 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) = 0.8800, rainfall intensity (i) = 5.7000 in/hr, peak discharge (Q) = 543.7 cfs.

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

5. Step 5 — Evaluate:

   $$A = 108.4\ \text{acre}$$

6. Step 6 — Check: returning A = 108.4 acre to

   $$Q = C i A$$

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

Why the other options are there

• 216.8 — kept a factor of two that cancels in the correct rearrangement.
• 54.1966 — dropped that same factor in the other direction.
• 119.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.7400; rainfall intensity (i) = 2.5000 in/hr; drainage area (A) = 189.0 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) = 0.7400, rainfall intensity (i) = 2.5000 in/hr, drainage area (A) = 189.0 acre.

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

5. Step 5 — Evaluate:

   $$Q = 349.7\ \text{cfs}$$

6. Step 6 — Check: returning Q = 349.7 cfs to

   $$Q = C i A$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given rainfall intensity (i) = 3.3000 in/hr; drainage area (A) = 147.0 acre; peak discharge (Q) = 655.9 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) = 3.3000 in/hr, drainage area (A) = 147.0 acre, peak discharge (Q) = 655.9 cfs.

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

5. Step 5 — Evaluate:

   $$C = 1.3521$$

6. Step 6 — Check: returning C = 1.3521 to

   $$Q = C i A$$

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

Why the other options are there

• 2.7042 — kept a factor of two that cancels in the correct rearrangement.
• 0.6760 — dropped that same factor in the other direction.
• 1.4873 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.9200; drainage area (A) = 12.0000 acre; peak discharge (Q) = 219.1 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) = 0.9200, drainage area (A) = 12.0000 acre, peak discharge (Q) = 219.1 cfs.

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

5. Step 5 — Evaluate:

   $$i = 19.8460\ \text{in/hr}$$

6. Step 6 — Check: returning i = 19.8460 in/hr to

   $$Q = C i A$$

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

Why the other options are there

• 39.6920 — kept a factor of two that cancels in the correct rearrangement.
• 9.9230 — dropped that same factor in the other direction.
• 21.8306 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.4900; rainfall intensity (i) = 1.4000 in/hr; peak discharge (Q) = 24.0000 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) = 0.4900, rainfall intensity (i) = 1.4000 in/hr, peak discharge (Q) = 24.0000 cfs.

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

5. Step 5 — Evaluate:

   $$A = 34.9854\ \text{acre}$$

6. Step 6 — Check: returning A = 34.9854 acre to

   $$Q = C i A$$

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

Why the other options are there

• 69.9708 — kept a factor of two that cancels in the correct rearrangement.
• 17.4927 — dropped that same factor in the other direction.
• 38.4840 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula

A hydrology and water resources problem uses Rational method. Given runoff coefficient (C) = 0.6200; rainfall intensity (i) = 4.5000 in/hr; drainage area (A) = 151.0 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) = 0.6200, rainfall intensity (i) = 4.5000 in/hr, drainage area (A) = 151.0 acre.

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

5. Step 5 — Evaluate:

   $$Q = 421.3\ \text{cfs}$$

6. Step 6 — Check: returning Q = 421.3 cfs to

   $$Q = C i A$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Hydrology and Water Resources → Rational Formula