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
vd = 20 mmh = 1 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 1 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 1 mg = 9.81 m/s²d = 20 mm
Q = L/s
2.Easy
12Q = 32 L/sv = 3 m/s, d = ?

A water line must carry 32 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 32 L/sv = 3 m/s
d = mm
3.Medium
12d1​ = 100 mm, p1​ = 200 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 200 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 200 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.61h = 6 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 6 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 6 mCd = 0.61g = 9.81 m/s²
Q = L/s
5.Hard
H = ?d1​ = 50 mmp1​ = 110 kPad2​ = 25 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 50 mm and a gauge pressure of 110 kPa. The nozzle exit diameter is 25 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 50 mmp1 = 110 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 75 mm, p1​ = 190 kPad2​ = 50 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 7 m. At section 1 the pressure is 190 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 190 kPav1 = 2.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 1.392 L/s
  2. 2. d = 116.5 mm
  3. 3. p2 = 198.3 kPa
  4. 4. Q = 3.249 L/s
  5. 5. H = 11.96 m
  6. 6. p2 = 108.6 kPa

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