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​ = 150 mm, v1​ = 2.75 m/sd2​ = 75 mm

Water flows at 2.75 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 2.75 m/s
Q = L/s
2.Easy
12Q = 57 L/sv = 1.5 m/s, d = ?

A water line must carry 57 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 57 L/sv = 1.5 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 260 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 260 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 260 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 150 mmd2​ = 100 mm12p1​ − p2​ = 43 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 100 mm. The pressure at the inlet is 43 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 100 mmp1 − p2 = 43 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
C211 m4.5 md = 40 mmpC​ = ?

A hose with an inner diameter of 40 mm siphons water from an open tank. The highest point C of the hose is 1 m above the water surface, and the outlet (open to the air) is 4.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 40 mmzC = +1 mz2 = −4.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 100 mm, p1​ = 380 kPad2​ = 75 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 7 m. At section 1 the pressure is 380 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 380 kPav1 = 2.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 48.6 L/s
  2. 2. d = 220 mm
  3. 3. p2 = 259.5 kPa
  4. 4. Q = 81.31 L/s
  5. 5. pC = 47.34 kPa
  6. 6. p2 = 304.6 kPa

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