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​ = 0.75 m/sd2​ = 40 mm

Water flows at 0.75 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 = 40 mmv1 = 0.75 m/s
Q = L/s
2.Easy
vd = 10 mmh = 4 m

An open water tank drains through a round opening with a diameter of 10 mm in its side. The free surface is 4 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 4 mg = 9.81 m/s²d = 10 mm
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 35 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 35 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 35 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 50 mm, p2​ = 240 kPa

Water flows at 8 L/s through a horizontal pipe that narrows from 100 mm to 50 mm. The pressure in the narrow section is 240 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 8 L/sd1 = 100 mmd2 = 50 mmp2 = 240 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 350 kPad2​ = 40 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 9 m. At section 1 the pressure is 350 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 350 kPav1 = 1 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 50 mmp1​ = 80 kPad2​ = 30 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 80 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 = 50 mmp1 = 80 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 3.313 L/s
  2. 2. Q = 0.6958 L/s
  3. 3. v = 8.367 m/s
  4. 4. p1 = 247.8 kPa
  5. 5. p2 = 163.3 kPa
  6. 6. H = 9.369 m

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