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​ = 200 mm, v1​ = 2 m/sd2​ = 100 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 2 m/s
Q = L/s
2.Easy
12d1​ = 200 mm, v1​ = 1.25 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = 150 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 150 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 150 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 50 mm, Cd​ = 0.64h = 2.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 2.5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 2.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
d1​ = 150 mmd2​ = 75 mm12Δh = 200 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 200 mm. The discharge coefficient is 0.98. 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 = 200 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 270 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 5 m. At section 1 the pressure is 270 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 270 kPav1 = 0.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 62.83 L/s
  2. 2. v2 = 8.889 m/s
  3. 3. p2 = 136.1 kPa
  4. 4. Q = 8.801 L/s
  5. 5. Q = 31.44 L/s
  6. 6. p2 = 219.8 kPa

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