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 = 51 L/sv = 1.5 m/s, d = ?

A water line must carry 51 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 51 L/sv = 1.5 m/s
d = mm
2.Easy
12Q = 23 L/sv = 1 m/s, d = ?

A water line must carry 23 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 23 L/sv = 1 m/s
d = mm
3.Medium
12d1​ = 80 mm, p1​ = ?d2​ = 40 mm, p2​ = 130 kPa

Water flows at 8 L/s through a horizontal pipe that narrows from 80 mm to 40 mm. The pressure in the narrow section is 130 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 8 L/sd1 = 80 mmd2 = 40 mmp2 = 130 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
Q = ?d = 40 mm, Cd​ = 0.65h = 4.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 4.5 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 4.5 mCd = 0.65g = 9.81 m/s²
Q = L/s
5.Hard
C212.5 m2.5 md = 50 mmpC​ = ?

A hose with an inner diameter of 50 mm siphons water from an open tank. The highest point C of the hose is 2.5 m above the water surface, and the outlet (open to the air) is 2.5 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 = 50 mmzC = +2.5 mz2 = −2.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
pair​ = 140 kPaQ = ?d = 30 mmh = 1 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 30 mm, 1 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 = 1 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. d = 208.1 mm
  2. 2. d = 171.1 mm
  3. 3. p1 = 149 kPa
  4. 4. Q = 7.675 L/s
  5. 5. pC = 52.25 kPa
  6. 6. Q = 12.24 L/s

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