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Drag Equation worksheet

Grades 11–12 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Drag coefficient
- Drag force (F): 375 N
- Fluid density (ρ): 1.3 kg/m³
- Speed relative to the fluid (v): 35 m/s
- Reference (frontal) area (A): 1.6 m²
Find: Drag coefficient
Answer
2.
Problem 2.
- Solve for: Drag force
- Fluid density (ρ): 1.12 kg/m³
- Speed relative to the fluid (v): 34 m/s
- Drag coefficient (Cd): 0.3
- Reference (frontal) area (A): 2.2 m²
- Show force in: Kilonewtons (kN)
Find: Drag force
Answer
3.
Problem 3.
- Solve for: Area
- Drag force (F): 340 N
- Fluid density (ρ): 1.1 kg/m³
- Speed relative to the fluid (v): 20 m/s
- Drag coefficient (Cd): 0.4
- Show area in: Square meters (m²)
Find: Reference area
Answer
4.
Problem 4.
- Solve for: Speed
- Drag force (F): 500 N
- Fluid density (ρ): 1.8 kg/m³
- Drag coefficient (Cd): 0.3
- Reference (frontal) area (A): 2.8 m²
- Show speed in: Kilometers per hour (km/h)
Find: Speed
Answer
5.
Problem 5.
- Solve for: Drag coefficient
- Drag force (F): 440 N
- Fluid density (ρ): 1 kg/m³
- Speed relative to the fluid (v): 32 m/s
- Reference (frontal) area (A): 2.6 m²
Find: Drag coefficient
Answer
6.
Problem 6.
- Solve for: Speed
- Drag force (F): 320 N
- Fluid density (ρ): 0.85 kg/m³
- Drag coefficient (Cd): 0.3
- Reference (frontal) area (A): 2 m²
- Show speed in: Knots (kn)
Find: Speed
Answer
7.
Problem 7.
- Solve for: Speed
- Drag force (F): 420 N
- Fluid density (ρ): 1.2 kg/m³
- Drag coefficient (Cd): 0.3
- Reference (frontal) area (A): 2.5 m²
- Show speed in: Knots (kn)
Find: Speed
Answer
8.
Problem 8.
- Solve for: Drag force
- Fluid density (ρ): 1.35 kg/m³
- Speed relative to the fluid (v): 40 m/s
- Drag coefficient (Cd): 0.2
- Reference (frontal) area (A): 2.8 m²
- Show force in: Kilonewtons (kN)
Find: Drag force
Answer
9.
Problem 9.
- Solve for: Speed
- Drag force (F): 330 N
- Fluid density (ρ): 1.1 kg/m³
- Drag coefficient (Cd): 0.3
- Reference (frontal) area (A): 2.2 m²
- Show speed in: Meters per second (m/s)
Find: Speed
Answer
10.
Problem 10.
- Solve for: Drag force
- Fluid density (ρ): 1.15 kg/m³
- Speed relative to the fluid (v): 36 m/s
- Drag coefficient (Cd): 0.2
- Reference (frontal) area (A): 2.4 m²
- Show force in: Newtons (N)
Find: Drag force
Answer

Answer key: Drag Equation worksheet

1. Drag coefficient: 0.29
1. Turn the drag equation around to solve for the shape number Cd. Double the force, then divide by density × speed squared × area
  $\frac{2 \times 375}{1.3 \times 35^{2} \times 1.6}$ $= 0.294349$
2. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $375 \times 35$ $= 13,125 W$
2. Drag force: 0.43 kN
1. Multiply half the density (ρ) by the speed squared (v²), the shape number (Cd) and the area (A). That gives the drag force F
  $0.5 \times 1.12 \times 34^{2} \times 0.3 \times 2.2$ $= 427.2576 N$
2. Change the answer to kN, the unit you picked: divide by 1,000
  $\frac{427.2576}{1,000}$ $= 0.427258 kN$
3. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $427.2576 \times 34$ $= 14,526.7584 W$
3. Reference area: 3.86 m²
1. Turn the drag equation around to solve for the area. Double the force, then divide by density × speed squared × Cd
  $\frac{2 \times 340}{1.1 \times 20^{2} \times 0.4}$ $= 3.863636 m²$
2. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $340 \times 20$ $= 6,800 W$
4. Speed: 92.58 km/h
1. Turn the drag equation around to solve for speed. Double the force, divide by density × Cd × area, then take the square root
  $\sqrt{\frac{2 \times 500}{1.8 \times 0.3 \times 2.8}}$ $= 25.717225 m/s$
2. Change the answer to km/h, the unit you picked: divide by 0.277777777778
  $\frac{25.717225}{0.277777777778}$ $= 92.58201 km/h$
3. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $500 \times 25.717225$ $= 12,858.612497 W$
5. Drag coefficient: 0.33
1. Turn the drag equation around to solve for the shape number Cd. Double the force, then divide by density × speed squared × area
  $\frac{2 \times 440}{1 \times 32^{2} \times 2.6}$ $= 0.330529$
2. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $440 \times 32$ $= 14,080 W$
6. Speed: 68.86 kn
1. Turn the drag equation around to solve for speed. Double the force, divide by density × Cd × area, then take the square root
  $\sqrt{\frac{2 \times 320}{0.85 \times 0.3 \times 2}}$ $= 35.424595 m/s$
2. Change the answer to kn, the unit you picked: divide by 0.514444444444
  $\frac{35.424595}{0.514444444444}$ $= 68.859905 kn$
3. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $320 \times 35.424595$ $= 11,335.870535 W$
7. Speed: 59.39 kn
1. Turn the drag equation around to solve for speed. Double the force, divide by density × Cd × area, then take the square root
  $\sqrt{\frac{2 \times 420}{1.2 \times 0.3 \times 2.5}}$ $= 30.550505 m/s$
2. Change the answer to kn, the unit you picked: divide by 0.514444444444
  $\frac{30.550505}{0.514444444444}$ $= 59.38543 kn$
3. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $420 \times 30.550505$ $= 12,831.211946 W$
8. Drag force: 0.6 kN
1. Multiply half the density (ρ) by the speed squared (v²), the shape number (Cd) and the area (A). That gives the drag force F
  $0.5 \times 1.35 \times 40^{2} \times 0.2 \times 2.8$ $= 604.8 N$
2. Change the answer to kN, the unit you picked: divide by 1,000
  $\frac{604.8}{1,000}$ $= 0.6048 kN$
3. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $604.8 \times 40$ $= 24,192 W$
9. Speed: 30.15 m/s
1. Turn the drag equation around to solve for speed. Double the force, divide by density × Cd × area, then take the square root
  $\sqrt{\frac{2 \times 330}{1.1 \times 0.3 \times 2.2}}$ $= 30.151134 m/s$
2. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $330 \times 30.151134$ $= 9,949.874371 W$
10. Drag force: 357.7 N
1. Multiply half the density (ρ) by the speed squared (v²), the shape number (Cd) and the area (A). That gives the drag force F
  $0.5 \times 1.15 \times 36^{2} \times 0.2 \times 2.4$ $= 357.696 N$
2. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts
  $357.696 \times 36$ $= 12,877.056 W$