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
vd = 20 mmh = 8 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 8 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 8 mg = 9.81 m/s²d = 20 mm
Q = L/s
2.Easy
12d = 200 mm, v = 0.5 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 0.5 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 0.5 m/sd = 200 mm
ṁ = kg/s
3.Medium
12d1​ = 75 mm, p1​ = 230 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 230 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 230 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 270 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 270 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 270 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 240 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 4 m. At section 1 the pressure is 240 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 240 kPav1 = 2 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C211.5 m3.5 md = 25 mmQ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 1.5 m above the water surface, and the outlet (open to the air) is 3.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 25 mmzC = +1.5 mz2 = −3.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 3.936 L/s
  2. 2. ṁ = 13.82 kg/s
  3. 3. p2 = 226.8 kPa
  4. 4. p2 = 213.3 kPa
  5. 5. p2 = 101.6 kPa
  6. 6. Q = 4.068 L/s

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