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 = 4 m

An open water tank drains through a small opening in its side. The free surface is 4 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 4 mg = 9.81 m/s²
v = m/s
2.Easy
12d = 80 mm, v = 3.5 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 3.5 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 3.5 m/sd = 80 mm
ṁ = kg/s
3.Medium
d1​ = 250 mmd2​ = 125 mm12p1​ − p2​ = 36 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 250 mm and a throat diameter of 125 mm. The pressure at the inlet is 36 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 250 mmd2 = 125 mmp1 − p2 = 36 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 390 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 390 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 390 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 250 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 7 m. At section 1 the pressure is 250 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 250 kPav1 = 2.75 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 330 kPad2​ = 25 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 7 m. At section 1 the pressure is 330 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 330 kPav1 = 1.25 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 8.859 m/s
  2. 2. ṁ = 22.17 kg/s
  3. 3. Q = 107.5 L/s
  4. 4. p2 = 367.5 kPa
  5. 5. p2 = 138.4 kPa
  6. 6. p2 = 198.8 kPa

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