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
12d1​ = 75 mm, v1​ = 0.75 m/sd2​ = 25 mm

Water flows at 0.75 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 25 mmv1 = 0.75 m/s
Q = L/s
2.Easy
vd = 20 mmh = 2.5 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 2.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2.5 mg = 9.81 m/s²d = 20 mm
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 210 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 210 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 210 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.6h = 5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 5 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 5 mCd = 0.6g = 9.81 m/s²
Q = L/s
5.Hard
C210.5 m1 md = 32 mmQ = ?

A hose with an inner diameter of 32 mm siphons water from an open tank. The highest point C of the hose is 0.5 m above the water surface, and the outlet (open to the air) is 1 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 32 mmzC = +0.5 mz2 = −1 mg = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 150 mm, p1​ = 330 kPad2​ = 100 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 6 m. At section 1 the pressure is 330 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 330 kPav1 = 1 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 3.313 L/s
  2. 2. Q = 2.2 L/s
  3. 3. p2 = 198.3 kPa
  4. 4. Q = 2.917 L/s
  5. 5. Q = 3.562 L/s
  6. 6. p2 = 269.1 kPa

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