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
12d = 150 mm, v = 2.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 2.25 m/sd = 150 mm
ṁ = kg/s
2.Easy
12Q = 15 L/sv = 1 m/s, d = ?

A water line must carry 15 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 15 L/sv = 1 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = 290 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 290 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 290 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 230 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 230 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 230 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C213 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 3 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 = +3 mz2 = −2.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 150 mm, p1​ = 260 kPad2​ = 100 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 6 m. At section 1 the pressure is 260 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 260 kPav1 = 1 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 50.1 kg/s
  2. 2. d = 138.2 mm
  3. 3. p2 = 281.9 kPa
  4. 4. p2 = 207 kPa
  5. 5. pC = 47.34 kPa
  6. 6. p2 = 199.1 kPa

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