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 = 100 mm, v = 2 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 2 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 2 m/sd = 100 mm
ṁ = kg/s
2.Easy
vd = 20 mmh = 2 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 2 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2 mg = 9.81 m/s²d = 20 mm
Q = L/s
3.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 52 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 52 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 52 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
Q = ?d = 30 mm, Cd​ = 0.65h = 5.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 5.5 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 5.5 mCd = 0.65g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 150 mm, p1​ = 160 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 4 m. At section 1 the pressure is 160 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 160 kPav1 = 2.75 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 140 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 140 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 140 kPav1 = 1.5 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 15.71 kg/s
  2. 2. Q = 1.968 L/s
  3. 3. Q = 186.1 L/s
  4. 4. Q = 4.773 L/s
  5. 5. p2 = 64.04 kPa
  6. 6. p2 = 34.83 kPa

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