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
12Q = 18 L/sv = 1 m/s, d = ?

A water line must carry 18 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 18 L/sv = 1 m/s
d = mm
2.Easy
vd = 40 mmh = 1 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 1 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 1 mg = 9.81 m/s²d = 40 mm
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 340 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 340 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 340 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 26 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 26 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 26 kPaρ = 1000 kg/m³
v = m/s
5.Hard
H = ?d1​ = 75 mmp1​ = 120 kPad2​ = 20 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 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 = 75 mmp1 = 120 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 150 mm, p1​ = 250 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 7 m. At section 1 the pressure is 250 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 250 kPav1 = 2.25 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 151.4 mm
  2. 2. Q = 5.566 L/s
  3. 3. p2 = 283.3 kPa
  4. 4. v = 7.211 m/s
  5. 5. H = 12.29 m
  6. 6. p2 = 171 kPa

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