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
12d1​ = 75 mm, v1​ = 2 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 2 m/s
v2 = m/s
2.Easy
v = ?h = 7.5 m

An open water tank drains through a small opening in its side. The free surface is 7.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 7.5 mg = 9.81 m/s²
v = m/s
3.Medium
v = ?p0​pp0​ − p = 1150 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1150 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1150 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 150 mm, p1​ = 110 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 110 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 110 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 170 kPad2​ = 75 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 1 m. At section 1 the pressure is 170 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 170 kPav1 = 0.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 150 mmd2​ = 75 mm12Δh = 240 mmmercuryQ = ?

A horizontal venturi meter (inlet 150 mm, throat 75 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 240 mm. The discharge coefficient is 0.97. 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 = 150 mmd2 = 75 mmΔh = 240 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 7.031 m/s
  2. 2. v = 12.13 m/s
  3. 3. v = 43.78 m/s
  4. 4. p2 = 91.72 kPa
  5. 5. p2 = 158.3 kPa
  6. 6. Q = 34.09 L/s

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