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 = 41 L/sv = 2 m/s, d = ?

A water line must carry 41 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 41 L/sv = 2 m/s
d = mm
2.Easy
vd = 30 mmh = 2.5 m

An open water tank drains through a round opening with a diameter of 30 mm in its side. The free surface is 2.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2.5 mg = 9.81 m/s²d = 30 mm
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 60 kPa

Water flows at 20 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 60 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 20 L/sd1 = 100 mmd2 = 75 mmp2 = 60 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
Q = ?d = 20 mm, Cd​ = 0.63h = 2 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 2 m above the orifice and the discharge coefficient is 0.63. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 2 mCd = 0.63g = 9.81 m/s²
Q = L/s
5.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 240 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 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 0.95. 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 = 100 mmd2 = 50 mmΔh = 240 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 150 mm, p1​ = 160 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 7 m. At section 1 the pressure is 160 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 160 kPav1 = 0.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 161.6 mm
  2. 2. Q = 4.951 L/s
  3. 3. p1 = 67 kPa
  4. 4. Q = 1.24 L/s
  5. 5. Q = 14.84 L/s
  6. 6. p2 = 66.74 kPa

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