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 = 38 L/sv = 2.5 m/s, d = ?

A water line must carry 38 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 38 L/sv = 2.5 m/s
d = mm
2.Easy
12d1​ = 75 mm, v1​ = 2 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 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 2 m/s
v2 = m/s
3.Medium
Q = ?d = 50 mm, Cd​ = 0.61h = 1.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 1.5 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 1.5 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 150 mm, p1​ = 260 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 260 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 260 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C212.5 m5 md = 32 mmpC​ = ?

A hose with an inner diameter of 32 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 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 = 32 mmzC = +2.5 mz2 = −5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 75 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 5 m. At section 1 the pressure is 280 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 280 kPav1 = 1 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 139.1 mm
  2. 2. v2 = 7.031 m/s
  3. 3. Q = 6.498 L/s
  4. 4. p2 = 252.5 kPa
  5. 5. pC = 27.72 kPa
  6. 6. p2 = 228.9 kPa

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