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​ = 2.25 m/sd2​ = 50 mm

Water flows at 2.25 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 = 50 mmv1 = 2.25 m/s
Q = L/s
2.Easy
12Q = 59 L/sv = 1.5 m/s, d = ?

A water line must carry 59 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 59 L/sv = 1.5 m/s
d = mm
3.Medium
d1​ = 250 mmd2​ = 125 mm12p1​ − p2​ = 39 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 39 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 250 mmd2 = 125 mmp1 − p2 = 39 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 180 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 180 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 180 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 100 kPad2​ = 50 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 7 m. At section 1 the pressure is 100 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 100 kPav1 = 0.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C213 m2 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 3 m above the water surface, and the outlet (open to the air) is 2 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 20 mmzC = +3 mz2 = −2 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 9.94 L/s
  2. 2. d = 223.8 mm
  3. 3. Q = 111.9 L/s
  4. 4. p2 = 117.5 kPa
  5. 5. p2 = 21.33 kPa
  6. 6. Q = 1.968 L/s

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