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​ = 75 mm, v1​ = 3 m/sd2​ = 50 mm

Water flows at 3 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 3 m/s
Q = L/s
2.Easy
12Q = 38 L/sv = 2.5 m/s, d = ?

A water line must carry 38 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 38 L/sv = 2.5 m/s
d = mm
3.Medium
12d1​ = 100 mm, p1​ = 170 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 170 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 170 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 49 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 300 mm and a throat diameter of 150 mm. The pressure at the inlet is 49 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 49 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 220 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 9 m. At section 1 the pressure is 220 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 220 kPav1 = 1.25 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 100 mmp1​ = 70 kPad2​ = 25 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 70 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 = 100 mmp1 = 70 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 13.25 L/s
  2. 2. d = 139.1 mm
  3. 3. p2 = 161.8 kPa
  4. 4. Q = 180.7 L/s
  5. 5. p2 = 120 kPa
  6. 6. H = 7.164 m

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