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​ = 75 mm, v1​ = 2.75 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 2.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 2.75 m/s
v2 = m/s
2.Easy
12d = 80 mm, v = 0.5 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 0.5 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 0.5 m/sd = 80 mm
ṁ = kg/s
3.Medium
12d1​ = 75 mm, p1​ = 350 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 350 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 350 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 29 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 29 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 29 kPaρ = 1000 kg/m³
v = m/s
5.Hard
C211.5 m4.5 md = 25 mmQ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 1.5 m above the water surface, and the outlet (open to the air) is 4.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 25 mmzC = +1.5 mz2 = −4.5 mg = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 200 kPad2​ = 75 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 10 m. At section 1 the pressure is 200 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 200 kPav1 = 1 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 6.188 m/s
  2. 2. ṁ = 2.212 kg/s
  3. 3. p2 = 340 kPa
  4. 4. v = 7.616 m/s
  5. 5. Q = 4.612 L/s
  6. 6. p2 = 77.12 kPa

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