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​ = 150 mm, v1​ = 2.25 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 2.25 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 2.25 m/s
v2 = m/s
2.Easy
12Q = 42 L/sv = 2 m/s, d = ?

A water line must carry 42 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 42 L/sv = 2 m/s
d = mm
3.Medium
d1​ = 150 mmd2​ = 75 mm12p1​ − p2​ = 9 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 75 mm. The pressure at the inlet is 9 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 75 mmp1 − p2 = 9 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
Q = ?d = 50 mm, Cd​ = 0.64h = 1.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 1.5 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 = 1.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
H = ?d1​ = 75 mmp1​ = 80 kPad2​ = 20 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 75 mm and a gauge pressure of 80 kPa. The nozzle exit diameter is 20 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 = 75 mmp1 = 80 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
H = ?d1​ = 75 mmp1​ = 140 kPad2​ = 25 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 75 mm and a gauge pressure of 140 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 = 75 mmp1 = 140 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. v2 = 5.063 m/s
  2. 2. d = 163.5 mm
  3. 3. Q = 19.36 L/s
  4. 4. Q = 6.817 L/s
  5. 5. H = 8.196 m
  6. 6. H = 14.45 m

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