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​ = 100 mm, v1​ = 2 m/sd2​ = 50 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 50 mmv1 = 2 m/s
Q = L/s
2.Easy
12Q = 56 L/sv = 1 m/s, d = ?

A water line must carry 56 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 56 L/sv = 1 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 140 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 140 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 140 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 180 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 180 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 180 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C210.5 m3 md = 32 mmpC​ = ?

A hose with an inner diameter of 32 mm siphons water from an open tank. The highest point C of the hose is 0.5 m above the water surface, and the outlet (open to the air) is 3 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 32 mmzC = +0.5 mz2 = −3 mg = 9.81 m/s²patm = 101.3 kPa
pC = 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 = 15.71 L/s
  2. 2. d = 267 mm
  3. 3. p2 = 136.8 kPa
  4. 4. p2 = 176.8 kPa
  5. 5. pC = 66.97 kPa
  6. 6. H = 9.369 m

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