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​ = 1 m/sd2​ = 50 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 1 m/s
Q = L/s
2.Easy
12Q = 49 L/sv = 1.5 m/s, d = ?

A water line must carry 49 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 49 L/sv = 1.5 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = 230 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 230 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 230 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 1150 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1150 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1150 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 150 mm, p1​ = 290 kPad2​ = 100 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 8 m. At section 1 the pressure is 290 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 290 kPav1 = 2.25 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 50 mmp1​ = 90 kPad2​ = 25 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 50 mm and a gauge pressure of 90 kPa. The nozzle exit diameter is 25 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 50 mmp1 = 90 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 4.418 L/s
  2. 2. d = 203.9 mm
  3. 3. p2 = 214.6 kPa
  4. 4. v = 43.78 m/s
  5. 5. p2 = 201.2 kPa
  6. 6. H = 9.786 m

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