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
12d1​ = 100 mm, v1​ = 0.75 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 0.75 m/s
v2 = m/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.61h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 1 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 400 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 400 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 400 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 75 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 6 m. At section 1 the pressure is 350 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 350 kPav1 = 2.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 100 mmp1​ = 120 kPad2​ = 20 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 20 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 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 4.418 L/s
  2. 2. v2 = 3 m/s
  3. 3. Q = 0.8488 L/s
  4. 4. v = 25.82 m/s
  5. 5. p2 = 275.8 kPa
  6. 6. H = 12.25 m

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