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​ = 200 mm, v1​ = 2.25 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 100 mm in diameter. The velocity in the wide section is 2.25 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 100 mmv1 = 2.25 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 2.25 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 2.25 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 2.25 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = 350 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 350 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 350 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 230 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 230 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 230 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 230 mmmercuryQ = ?

A horizontal venturi meter (inlet 80 mm, throat 40 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 230 mm. The discharge coefficient is 0.95. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 80 mmd2 = 40 mmΔh = 230 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
H = ?d1​ = 50 mmp1​ = 130 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 130 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 = 130 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. v2 = 9 m/s
  2. 2. v2 = 4 m/s
  3. 3. p2 = 250.9 kPa
  4. 4. p2 = 217.3 kPa
  5. 5. Q = 9.297 L/s
  6. 6. H = 14.14 m

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