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 = 30 mmh = 2 m

An open water tank drains through a round opening with a diameter of 30 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 = 30 mm
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 380 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 380 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 380 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 280 kPa

Water flows at 30 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 280 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 30 L/sd1 = 100 mmd2 = 75 mmp2 = 280 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
C212 m1.5 md = 20 mmQ = ?

A hose with an inner diameter of 20 mm siphons water from an open tank. The highest point C of the hose is 2 m above the water surface, and the outlet (open to the air) is 1.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 20 mmzC = +2 mz2 = −1.5 mg = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 220 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 5 m. At section 1 the pressure is 220 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 220 kPav1 = 1 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 4.428 L/s
  2. 2. v2 = 4.395 m/s
  3. 3. p2 = 340 kPa
  4. 4. p1 = 295.8 kPa
  5. 5. Q = 1.704 L/s
  6. 6. p2 = 146.2 kPa

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