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​ = 100 mm, v1​ = 2.75 m/sd2​ = 50 mm

Water flows at 2.75 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 50 mmv1 = 2.75 m/s
Q = L/s
2.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
3.Medium
v = ?p0​pp0​ − p = 26 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 26 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 26 kPaρ = 1000 kg/m³
v = m/s
4.Medium
Q = ?d = 20 mm, Cd​ = 0.63h = 6 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 6 m above the orifice and the discharge coefficient is 0.63. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 6 mCd = 0.63g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 9 m. At section 1 the pressure is 350 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 350 kPav1 = 0.5 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 320 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 320 mm. The discharge coefficient is 0.95. 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 = 50 mmΔh = 320 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 21.6 L/s
  2. 2. Q = 9.94 L/s
  3. 3. v = 7.211 m/s
  4. 4. Q = 2.147 L/s
  5. 5. p2 = 261.2 kPa
  6. 6. Q = 17.13 L/s

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