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
12d = 50 mm, v = 3 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 3 m/sd = 50 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 2.5 m/sd2​ = 75 mm

Water flows at 2.5 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 2.5 m/s
Q = L/s
3.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 30 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 30 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 30 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 150 mm, p1​ = 320 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 50 mm. In the wide section the pressure is 320 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 320 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 330 kPad2​ = 50 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 3 m. At section 1 the pressure is 330 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 330 kPav1 = 2.25 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 75 mmp1​ = 90 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 90 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 = 90 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 5.89 kg/s
  2. 2. Q = 44.18 L/s
  3. 3. Q = 141.4 L/s
  4. 4. p2 = 230 kPa
  5. 5. p2 = 262.6 kPa
  6. 6. H = 9.289 m

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