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 = 100 mm, v = 2.25 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 2.25 m/sd = 100 mm
ṁ = kg/s
2.Easy
12Q = 46 L/sv = 1 m/s, d = ?

A water line must carry 46 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 46 L/sv = 1 m/s
d = mm
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 250 kPa

Water flows at 23 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 250 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 23 L/sd1 = 100 mmd2 = 75 mmp2 = 250 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
v = ?p0​pp0​ − p = 1350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1350 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 75 mm, p1​ = 320 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 1 m. At section 1 the pressure is 320 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 320 kPav1 = 0.75 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 75 mmp1​ = 120 kPad2​ = 25 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 75 mm and a gauge pressure of 120 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 = 75 mmp1 = 120 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 18.11 kg/s
  2. 2. d = 242 mm
  3. 3. p1 = 259.3 kPa
  4. 4. v = 47.43 m/s
  5. 5. p2 = 309 kPa
  6. 6. H = 12.39 m

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