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 = 40 mm, v = 3.5 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 3.5 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 3.5 m/sd = 40 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 1 m/sd2​ = 40 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 40 mmv1 = 1 m/s
Q = L/s
3.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
4.Medium
v = ?p0​pp0​ − p = 3 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 3 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 3 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 150 mm, p1​ = 200 kPad2​ = 75 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 8 m. At section 1 the pressure is 200 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 200 kPav1 = 1.75 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 100 mmp1​ = 120 kPad2​ = 30 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 120 kPa. The nozzle exit diameter is 30 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 = 100 mmp1 = 120 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 4.398 kg/s
  2. 2. Q = 17.67 L/s
  3. 3. v = 47.43 m/s
  4. 4. v = 2.449 m/s
  5. 5. p2 = 98.55 kPa
  6. 6. H = 12.33 m

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