Water flows at 0.25 m³/s from a 300 mm pipe (p₁ = 250 kPa) into a 200 mm pipe at the same elevation. Neglecting losses, what is p₂?

Start with the thinking

• Continuity gives both velocities; Bernoulli converts the velocity change to pressure.
• Same elevation means the z terms cancel.

Step-by-step solution

1. Areas

   $$A_{1} = \pi(0.30)^{2}/4 = 0.0707 m^{2} and A_{2} = \pi(0.20)^{2}/4 = 0.0314 m^{2}$$

2. Velocities

   $$V_{1} = 0.25/0.0707 = 3.54 m/s and V_{2} = 0.25/0.0314 = 7.96 m/s$$

3. Bernoulli

   $$p_{2} = p_{1} + \rho(V_{1}^{2} - V_{2}^{2})/2$$

4. Velocity terms

   $$(3.54^{2} - 7.96^{2})/2 = (12.5 - 63.4)/2 = -25.4 m^{2}/s^{2}$$

5. Result

   $$p_{2} = 250,000 + 1,000(-25.4) = 224,600 Pa = 225 kPa$$

Why the other options are there

• 275 kPa (sign of the velocity term reversed)
• 250 kPa (velocity change ignored)

Reference: FE Reference Handbook — Fluid Mechanics — Energy equation

A fluid mechanics problem uses Hydrostatic pressure. Given unit weight (gamma) = 57.0000 lb/ft³; depth (h) = 82.0000 ft, determine the pressure (p) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: unit weight (gamma) = 57.0000 lb/ft^{3}, depth (h) = 82.0000 ft$$

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

5. Step 5 — Evaluate:

   $$p = 4674\ \text{psf}$$

6. Step 6 — Check: returning p = 4,674 psf to

   $$p = \gamma h$$

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

Why the other options are there

• 9,348 — kept a factor of two that cancels in the correct rearrangement.
• 2,337 — dropped that same factor in the other direction.
• 5,141 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given depth (h) = 58.0000 ft; pressure (p) = 1,658 psf, determine the unit weight (gamma) in lb/ft³.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• Everything except gamma is given, so isolate gamma 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: depth (h) = 58.0000 ft, pressure (p) = 1,658 psf$$

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

5. Step 5 — Evaluate:

   $$\gamma = 28.5862\ \text{lb/ft³}$$

6. Step 6 — Check: returning gamma = 28.5862 lb/ft³ to

   $$p = \gamma h$$

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

Why the other options are there

• 57.1724 — kept a factor of two that cancels in the correct rearrangement.
• 14.2931 — dropped that same factor in the other direction.
• 31.4448 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given unit weight (gamma) = 62.0000 lb/ft³; pressure (p) = 3,325 psf, determine the depth (h) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• Everything except h is given, so isolate h 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: unit weight (gamma) = 62.0000 lb/ft^{3}, pressure (p) = 3,325 psf$$

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

5. Step 5 — Evaluate:

   $$h = 53.6290\ \text{ft}$$

6. Step 6 — Check: returning h = 53.6290 ft to

   $$p = \gamma h$$

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

Why the other options are there

• 107.3 — kept a factor of two that cancels in the correct rearrangement.
• 26.8145 — dropped that same factor in the other direction.
• 58.9919 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given unit weight (gamma) = 58.0000 lb/ft³; depth (h) = 71.5000 ft, determine the pressure (p) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: unit weight (gamma) = 58.0000 lb/ft^{3}, depth (h) = 71.5000 ft$$

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

5. Step 5 — Evaluate:

   $$p = 4147\ \text{psf}$$

6. Step 6 — Check: returning p = 4,147 psf to

   $$p = \gamma h$$

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

Why the other options are there

• 8,294 — kept a factor of two that cancels in the correct rearrangement.
• 2,074 — dropped that same factor in the other direction.
• 4,562 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given depth (h) = 18.5000 ft; pressure (p) = 5,648 psf, determine the unit weight (gamma) in lb/ft³.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• Everything except gamma is given, so isolate gamma 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: depth (h) = 18.5000 ft, pressure (p) = 5,648 psf$$

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

5. Step 5 — Evaluate:

   $$\gamma = 305.3\ \text{lb/ft³}$$

6. Step 6 — Check: returning gamma = 305.3 lb/ft³ to

   $$p = \gamma h$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given unit weight (gamma) = 64.5000 lb/ft³; pressure (p) = 5,875 psf, determine the depth (h) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• Everything except h is given, so isolate h 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: unit weight (gamma) = 64.5000 lb/ft^{3}, pressure (p) = 5,875 psf$$

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

5. Step 5 — Evaluate:

   $$h = 91.0853\ \text{ft}$$

6. Step 6 — Check: returning h = 91.0853 ft to

   $$p = \gamma h$$

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

Why the other options are there

• 182.2 — kept a factor of two that cancels in the correct rearrangement.
• 45.5426 — dropped that same factor in the other direction.
• 100.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given unit weight (gamma) = 57.0000 lb/ft³; depth (h) = 84.0000 ft, determine the pressure (p) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: unit weight (gamma) = 57.0000 lb/ft^{3}, depth (h) = 84.0000 ft$$

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

5. Step 5 — Evaluate:

   $$p = 4788\ \text{psf}$$

6. Step 6 — Check: returning p = 4,788 psf to

   $$p = \gamma h$$

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

Why the other options are there

• 9,576 — kept a factor of two that cancels in the correct rearrangement.
• 2,394 — dropped that same factor in the other direction.
• 5,267 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given depth (h) = 86.5000 ft; pressure (p) = 4,953 psf, determine the unit weight (gamma) in lb/ft³.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• Everything except gamma is given, so isolate gamma 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: depth (h) = 86.5000 ft, pressure (p) = 4,953 psf$$

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

5. Step 5 — Evaluate:

   $$\gamma = 57.2601\ \text{lb/ft³}$$

6. Step 6 — Check: returning gamma = 57.2601 lb/ft³ to

   $$p = \gamma h$$

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

Why the other options are there

• 114.5 — kept a factor of two that cancels in the correct rearrangement.
• 28.6301 — dropped that same factor in the other direction.
• 62.9861 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation

A fluid mechanics problem uses Hydrostatic pressure. Given unit weight (gamma) = 58.5000 lb/ft³; pressure (p) = 5,935 psf, determine the depth (h) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Hydrostatic pressure.
• Everything except h is given, so isolate h 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$p = \gamma h$$

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

3. Step 3

   $$List the givens: unit weight (gamma) = 58.5000 lb/ft^{3}, pressure (p) = 5,935 psf$$

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

5. Step 5 — Evaluate:

   $$h = 101.5\ \text{ft}$$

6. Step 6 — Check: returning h = 101.5 ft to

   $$p = \gamma h$$

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

Why the other options are there

• 202.9 — kept a factor of two that cancels in the correct rearrangement.
• 50.7265 — dropped that same factor in the other direction.
• 111.6 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Energy Equation