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 = 17 L/sv = 1.5 m/s, d = ?

A water line must carry 17 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 17 L/sv = 1.5 m/s
d = mm
2.Easy
12Q = 6 L/sv = 1 m/s, d = ?

A water line must carry 6 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 6 L/sv = 1 m/s
d = mm
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 240 kPa

Water flows at 11 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 240 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 11 L/sd1 = 200 mmd2 = 100 mmp2 = 240 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
d1​ = 200 mmd2​ = 150 mm12p1​ − p2​ = 8 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 150 mm. The pressure at the inlet is 8 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 150 mmp1 − p2 = 8 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 150 mmd2​ = 100 mm12Δh = 370 mmmercuryQ = ?

A horizontal venturi meter (inlet 150 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 370 mm. The discharge coefficient is 0.97. 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 = 150 mmd2 = 100 mmΔh = 370 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
H = ?d1​ = 75 mmp1​ = 70 kPad2​ = 40 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 70 kPa. The nozzle exit diameter is 40 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 = 70 kPa (gauge)d2 = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. d = 120.1 mm
  2. 2. d = 87.4 mm
  3. 3. p1 = 240.9 kPa
  4. 4. Q = 85.49 L/s
  5. 5. Q = 81.34 L/s
  6. 6. H = 7.764 m

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