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​ = 1.25 m/sd2​ = 25 mm

Water flows at 1.25 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 = 25 mmv1 = 1.25 m/s
Q = L/s
2.Easy
vd = 15 mmh = 8 m

An open water tank drains through a round opening with a diameter of 15 mm in its side. The free surface is 8 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 8 mg = 9.81 m/s²d = 15 mm
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 210 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 210 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 210 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 19 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 19 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 19 kPaρ = 1000 kg/m³
v = m/s
5.Hard
H = ?d1​ = 50 mmp1​ = 110 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 110 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 = 110 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 200 mm, p1​ = 380 kPad2​ = 100 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 4 m. At section 1 the pressure is 380 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 380 kPav1 = 0.75 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 5.522 L/s
  2. 2. Q = 2.214 L/s
  3. 3. p2 = 142.5 kPa
  4. 4. v = 6.164 m/s
  5. 5. H = 11.96 m
  6. 6. p2 = 336.5 kPa

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