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​ = 200 mm, v1​ = 1.5 m/sd2​ = 100 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 1.5 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 2.75 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 2.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 2.75 m/s
v2 = m/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 270 kPa

Water flows at 21 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 270 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 21 L/sd1 = 150 mmd2 = 75 mmp2 = 270 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 310 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 310 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 310 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C212 m4 md = 20 mmpC​ = ?

A hose with an inner diameter of 20 mm siphons water from an open tank. The highest point C of the hose is 2 m above the water surface, and the outlet (open to the air) is 4 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 = 20 mmzC = +2 mz2 = −4 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
pair​ = 100 kPav = ?d = 40 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 100 kPa. Water leaves through an opening with a diameter of 40 mm, 5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 100 kPa (gauge)h = 5 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. Q = 47.12 L/s
  2. 2. v2 = 9.668 m/s
  3. 3. p1 = 280.6 kPa
  4. 4. p2 = 287 kPa
  5. 5. pC = 42.44 kPa
  6. 6. v = 17.27 m/s

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