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​ = 1 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 1 m/s
v2 = m/s
2.Easy
12d1​ = 75 mm, v1​ = 2.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 2.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 2.5 m/s
v2 = m/s
3.Medium
d1​ = 250 mmd2​ = 125 mm12p1​ − p2​ = 5 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 5 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 250 mmd2 = 125 mmp1 − p2 = 5 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 18 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 18 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 18 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 180 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 7 m. At section 1 the pressure is 180 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 180 kPav1 = 1 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 170 kPaQ = ?d = 50 mmh = 4 m

A closed water tank has compressed air above the water at a gauge pressure of 170 kPa. Water leaves through an opening with a diameter of 50 mm, 4 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 170 kPa (gauge)h = 4 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 2.25 m/s
  2. 2. v2 = 5.625 m/s
  3. 3. Q = 40.08 L/s
  4. 4. v = 6 m/s
  5. 5. p2 = 92.3 kPa
  6. 6. Q = 40.17 L/s

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