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
12Q = 36 L/sv = 2.5 m/s, d = ?

A water line must carry 36 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 36 L/sv = 2.5 m/s
d = mm
2.Easy
12d1​ = 75 mm, v1​ = 0.75 m/sd2​ = 50 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 = 50 mmv1 = 0.75 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 27 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 27 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 27 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 140 kPa

Water flows at 22 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 140 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 22 L/sd1 = 150 mmd2 = 75 mmp2 = 140 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 170 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 60 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 170 mm. The discharge coefficient is 0.98. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 100 mmd2 = 60 mmΔh = 170 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 150 mm, p1​ = 150 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 5 m. At section 1 the pressure is 150 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 150 kPav1 = 1 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 135.4 mm
  2. 2. Q = 3.313 L/s
  3. 3. v = 7.348 m/s
  4. 4. p1 = 151.6 kPa
  5. 5. Q = 19.25 L/s
  6. 6. p2 = 93.45 kPa

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