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
12d = 50 mm, v = 2.25 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2.25 m/sd = 50 mm
ṁ = kg/s
2.Easy
vd = 10 mmh = 0.5 m

An open water tank drains through a round opening with a diameter of 10 mm in its side. The free surface is 0.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 0.5 mg = 9.81 m/s²d = 10 mm
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 290 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 290 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 290 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 320 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 320 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 320 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 340 kPad2​ = 75 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 2 m. At section 1 the pressure is 340 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 340 kPav1 = 1.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 90 kPaQ = ?d = 40 mmh = 2 m

A closed water tank has compressed air above the water at a gauge pressure of 90 kPa. Water leaves through an opening with a diameter of 40 mm, 2 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 90 kPa (gauge)h = 2 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 3.888 kg/s
  2. 2. Q = 0.246 L/s
  3. 3. p2 = 190.9 kPa
  4. 4. p2 = 290.3 kPa
  5. 5. p2 = 317.1 kPa
  6. 6. Q = 18.61 L/s

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