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 = 50 mm, v = 3.25 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 3.25 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 3.25 m/sd = 50 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 3 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 3 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 3 m/s
v2 = m/s
3.Medium
12d1​ = 100 mm, p1​ = 400 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 400 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 400 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 50 kPa

Water flows at 31 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 50 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 31 L/sd1 = 200 mmd2 = 100 mmp2 = 50 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
C213 m3 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 3 m above the water surface, and the outlet (open to the air) is 3 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 = +3 mz2 = −3 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 75 mm, p1​ = 320 kPad2​ = 40 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 10 m. At section 1 the pressure is 320 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 320 kPav1 = 2.25 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 5.616 kg/s
  2. 2. v2 = 10.55 m/s
  3. 3. p2 = 370 kPa
  4. 4. p1 = 57.3 kPa
  5. 5. pC = 42.44 kPa
  6. 6. p2 = 193.1 kPa

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