Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
12Q = 28 L/sv = 3 m/s, d = ?

A water line must carry 28 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 28 L/sv = 3 m/s
d = mm
2.Easy
12Q = 41 L/sv = 3 m/s, d = ?

A water line must carry 41 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 41 L/sv = 3 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 550 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 550 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 550 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 200 mm, p1​ = 310 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 310 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 310 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 200 mmd2​ = 150 mm12Δh = 260 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 260 mm. The discharge coefficient is 0.95. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 200 mmd2 = 150 mmΔh = 260 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 120 kPad2​ = 75 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 3 m. At section 1 the pressure is 120 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 120 kPav1 = 1 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 109 mm
  2. 2. d = 131.9 mm
  3. 3. v = 30.28 m/s
  4. 4. p2 = 298.3 kPa
  5. 5. Q = 162.8 L/s
  6. 6. p2 = 65.79 kPa

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