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
v = ?h = 6.5 m

An open water tank drains through a small opening in its side. The free surface is 6.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 6.5 mg = 9.81 m/s²
v = m/s
2.Easy
12Q = 47 L/sv = 1.5 m/s, d = ?

A water line must carry 47 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 47 L/sv = 1.5 m/s
d = mm
3.Medium
Q = ?d = 30 mm, Cd​ = 0.61h = 3.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 3.5 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 3.5 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 100 mm, p1​ = 320 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 320 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 320 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 2 m. At section 1 the pressure is 280 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 280 kPav1 = 0.5 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 100 mmp1​ = 40 kPad2​ = 40 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 40 kPa. The nozzle exit diameter is 40 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 = 100 mmp1 = 40 kPa (gauge)d2 = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. v = 11.29 m/s
  2. 2. d = 199.7 mm
  3. 3. Q = 3.573 L/s
  4. 4. p2 = 315.2 kPa
  5. 5. p2 = 259.9 kPa
  6. 6. H = 4.185 m

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