sprinkler K factors used to size a fire protection sprinkler head Given sprinkler K-factor (K) = 18.0000 gpm/psi^0.5; pressure at sprinkler (P) = 24.0000 psi, determine the discharge (Q) in gpm.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler K Factors.
• 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.
• Sprinkler K factors relate the discharge of a fire sprinkler head to the pressure at its orifice.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

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

3. Step 3

   $$List the givens: sprinkler K-factor (K) = 18.0000 gpm/psi^0.5, pressure at sprinkler (P) = 24.0000 psi$$

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

5. Step 5 — Evaluate:

   $$Q = 88.1816\ \text{gpm}$$

6. Step 6 — Check: returning Q = 88.1816 gpm to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 176.4 — kept a factor of two that cancels in the correct rearrangement.
• 44.0908 — dropped that same factor in the other direction.
• 96.9998 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

an upright sprinkler protecting a parking structure Given sprinkler K factor (K) = 5.4000 gpm/psi^0.5; residual pressure at the head (P) = 66.5000 psi, determine the discharge (Q) in gpm.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler discharge from the K factor.
• 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.
• A fire-protection sprinkler head discharges under the residual pressure at the head.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = K \sqrt{P}$$

3. Step 3 — List the givens: sprinkler K factor (K) = 5.4000 gpm/psi^0.5, residual pressure at the head (P) = 66.5000 psi.

4. Step 4 — Substitute the given values:

   $$Q = 5.4000 \sqrt{66.5000}$$

5. Step 5 — Evaluate:

   $$Q = 44.0357\ \text{gpm}$$

6. Step 6 — Check: returning Q = 44.0357 gpm to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 88.0713 — kept a factor of two that cancels in the correct rearrangement.
• 22.0178 — dropped that same factor in the other direction.
• 48.4392 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

sprinkler K factors for a standard-response sprinkler in a piping design Given pressure at sprinkler (P) = 60.0000 psi; discharge (Q) = 191.0 gpm, determine the sprinkler K-factor (K) in gpm/psi^0.5.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler K Factors.
• Everything except K is given, so isolate K 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.
• Sprinkler K factors relate the discharge of a fire sprinkler head to the pressure at its orifice.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

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

3. Step 3

   $$List the givens: pressure at sprinkler (P) = 60.0000 psi, discharge (Q) = 191.0 gpm$$

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

5. Step 5 — Evaluate:

   K = 24.6580\ \text{gpm/psi^0.5}

6. Step 6 — Check: returning K = 24.6580 gpm/psi^0.5 to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 49.3160 — kept a factor of two that cancels in the correct rearrangement.
• 12.3290 — dropped that same factor in the other direction.
• 27.1238 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

a sidewall sprinkler on a corridor main Given discharge (Q) = 24.6000 gpm; residual pressure at the head (P) = 80.0000 psi, determine the sprinkler K factor (K) in gpm/psi^0.5.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler discharge from the K factor.
• Everything except K is given, so isolate K 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.
• A fire-protection sprinkler head discharges under the residual pressure at the head.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

2. Step 2 — Rearrange symbolically for K:

   $$K = \dfrac{Q}{\sqrt{P}}$$

3. Step 3

   $$List the givens: discharge (Q) = 24.6000 gpm, residual pressure at the head (P) = 80.0000 psi$$

4. Step 4 — Substitute the given values:

   $$K = \dfrac{24.6000}{\sqrt{80.0000}}$$

5. Step 5 — Evaluate:

   K = 2.7504\ \text{gpm/psi^0.5}

6. Step 6 — Check: returning K = 2.7504 gpm/psi^0.5 to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 5.5007 — kept a factor of two that cancels in the correct rearrangement.
• 1.3752 — dropped that same factor in the other direction.
• 3.0254 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

sprinkler K factors used to verify discharge in a hydraulic calculation Given sprinkler K-factor (K) = 5.5000 gpm/psi^0.5; discharge (Q) = 141.0 gpm, determine the pressure at sprinkler (P) in psi.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler K Factors.
• Everything except P is given, so isolate P 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.
• Sprinkler K factors relate the discharge of a fire sprinkler head to the pressure at its orifice.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

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

3. Step 3

   $$List the givens: sprinkler K-factor (K) = 5.5000 gpm/psi^0.5, discharge (Q) = 141.0 gpm$$

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

5. Step 5 — Evaluate:

   $$P = 657.2\ \text{psi}$$

6. Step 6 — Check: returning P = 657.2 psi to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 1,314 — kept a factor of two that cancels in the correct rearrangement.
• 328.6 — dropped that same factor in the other direction.
• 722.9 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

a pendent sprinkler on a warehouse branch line Given discharge (Q) = 32.4000 gpm; sprinkler K factor (K) = 8.9000 gpm/psi^0.5, determine the residual pressure at the head (P) in psi.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler discharge from the K factor.
• Everything except P is given, so isolate P 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.
• A fire-protection sprinkler head discharges under the residual pressure at the head.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

2. Step 2 — Rearrange symbolically for P:

   $$P = \left(\dfrac{Q}{K}\right)^2$$

3. Step 3

   $$List the givens: discharge (Q) = 32.4000 gpm, sprinkler K factor (K) = 8.9000 gpm/psi^0.5$$

4. Step 4 — Substitute the given values:

   $$P = \left(\dfrac{32.4000}{8.9000}\right)^2$$

5. Step 5 — Evaluate:

   $$P = 13.2529\ \text{psi}$$

6. Step 6 — Check: returning P = 13.2529 psi to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 26.5057 — kept a factor of two that cancels in the correct rearrangement.
• 6.6264 — dropped that same factor in the other direction.
• 14.5782 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

sprinkler K factors used to size a fire protection sprinkler head Given sprinkler K-factor (K) = 4.0000 gpm/psi^0.5; pressure at sprinkler (P) = 69.0000 psi, determine the discharge (Q) in gpm.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler K Factors.
• 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.
• Sprinkler K factors relate the discharge of a fire sprinkler head to the pressure at its orifice.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

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

3. Step 3

   $$List the givens: sprinkler K-factor (K) = 4.0000 gpm/psi^0.5, pressure at sprinkler (P) = 69.0000 psi$$

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

5. Step 5 — Evaluate:

   $$Q = 33.2265\ \text{gpm}$$

6. Step 6 — Check: returning Q = 33.2265 gpm to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 66.4530 — kept a factor of two that cancels in the correct rearrangement.
• 16.6132 — dropped that same factor in the other direction.
• 36.5491 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

an upright sprinkler protecting a parking structure Given sprinkler K factor (K) = 11.4000 gpm/psi^0.5; residual pressure at the head (P) = 79.5000 psi, determine the discharge (Q) in gpm.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler discharge from the K factor.
• 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.
• A fire-protection sprinkler head discharges under the residual pressure at the head.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = K \sqrt{P}$$

3. Step 3 — List the givens: sprinkler K factor (K) = 11.4000 gpm/psi^0.5, residual pressure at the head (P) = 79.5000 psi.

4. Step 4 — Substitute the given values:

   $$Q = 11.4000 \sqrt{79.5000}$$

5. Step 5 — Evaluate:

   $$Q = 101.6\ \text{gpm}$$

6. Step 6 — Check: returning Q = 101.6 gpm to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 203.3 — kept a factor of two that cancels in the correct rearrangement.
• 50.8228 — dropped that same factor in the other direction.
• 111.8 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

sprinkler K factors for a standard-response sprinkler in a piping design Given pressure at sprinkler (P) = 66.0000 psi; discharge (Q) = 325.0 gpm, determine the sprinkler K-factor (K) in gpm/psi^0.5.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler K Factors.
• Everything except K is given, so isolate K 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.
• Sprinkler K factors relate the discharge of a fire sprinkler head to the pressure at its orifice.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

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

3. Step 3

   $$List the givens: pressure at sprinkler (P) = 66.0000 psi, discharge (Q) = 325.0 gpm$$

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

5. Step 5 — Evaluate:

   K = 40.0047\ \text{gpm/psi^0.5}

6. Step 6 — Check: returning K = 40.0047 gpm/psi^0.5 to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 80.0095 — kept a factor of two that cancels in the correct rearrangement.
• 20.0024 — dropped that same factor in the other direction.
• 44.0052 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors

a sidewall sprinkler on a corridor main Given discharge (Q) = 178.0 gpm; residual pressure at the head (P) = 71.5000 psi, determine the sprinkler K factor (K) in gpm/psi^0.5.

Start with the thinking

• The governing relation printed in this handbook section is Sprinkler discharge from the K factor.
• Everything except K is given, so isolate K 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.
• A fire-protection sprinkler head discharges under the residual pressure at the head.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = K \sqrt{P}$$

2. Step 2 — Rearrange symbolically for K:

   $$K = \dfrac{Q}{\sqrt{P}}$$

3. Step 3

   $$List the givens: discharge (Q) = 178.0 gpm, residual pressure at the head (P) = 71.5000 psi$$

4. Step 4 — Substitute the given values:

   $$K = \dfrac{178.0}{\sqrt{71.5000}}$$

5. Step 5 — Evaluate:

   K = 21.0507\ \text{gpm/psi^0.5}

6. Step 6 — Check: returning K = 21.0507 gpm/psi^0.5 to

   $$Q = K \sqrt{P}$$

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

Why the other options are there

• 42.1014 — kept a factor of two that cancels in the correct rearrangement.
• 10.5254 — dropped that same factor in the other direction.
• 23.1558 — rounded an intermediate value before the final step.

Reference: FE Handbook — Sprinkler K Factors