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​ = 75 mm, v1​ = 2 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 2 m/s
v2 = m/s
2.Easy
12d = 150 mm, v = 2 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 2 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 2 m/sd = 150 mm
ṁ = kg/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 260 kPa

Water flows at 27 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 260 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 27 L/sd1 = 150 mmd2 = 75 mmp2 = 260 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 270 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 270 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 270 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 130 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 1 m. At section 1 the pressure is 130 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 130 kPav1 = 3 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 75 mmp1​ = 150 kPad2​ = 30 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 150 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 = 75 mmp1 = 150 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. v2 = 7.031 m/s
  2. 2. ṁ = 35.34 kg/s
  3. 3. p1 = 277.5 kPa
  4. 4. p2 = 268 kPa
  5. 5. p2 = 69.07 kPa
  6. 6. H = 15.69 m

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