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​ = 0.75 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 0.75 m/s
v2 = m/s
2.Easy
12Q = 54 L/sv = 3 m/s, d = ?

A water line must carry 54 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 54 L/sv = 3 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 400 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 400 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 400 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 22 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 22 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 22 kPaρ = 1000 kg/m³
v = m/s
5.Hard
pair​ = 140 kPaQ = ?d = 25 mmh = 4 m

A closed water tank has compressed air above the water at a gauge pressure of 140 kPa. Water leaves through an opening with a diameter of 25 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 = 140 kPa (gauge)h = 4 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
C213 m1.5 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 3 m above the water surface, and the outlet (open to the air) is 1.5 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 = 20 mmzC = +3 mz2 = −1.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa

Answer key

  1. 1. v2 = 1.688 m/s
  2. 2. d = 151.4 mm
  3. 3. p2 = 384.6 kPa
  4. 4. v = 6.633 m/s
  5. 5. Q = 9.294 L/s
  6. 6. pC = 57.15 kPa

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