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​ = 3 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 3 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 100 mmv1 = 3 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 1.5 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 10 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 10 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 10 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 210 kPa

Water flows at 40 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 210 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 40 L/sd1 = 100 mmd2 = 75 mmp2 = 210 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
H = ?d1​ = 50 mmp1​ = 20 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 20 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 = 20 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 70 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 70 mm. The discharge coefficient is 0.96. 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 = 100 mmd2 = 50 mmΔh = 70 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 12 m/s
  2. 2. v2 = 6 m/s
  3. 3. v = 4.472 m/s
  4. 4. p1 = 238 kPa
  5. 5. H = 2.342 m
  6. 6. Q = 8.098 L/s

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