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​ = 2.75 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 2.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 2.75 m/s
v2 = m/s
2.Easy
12d = 200 mm, v = 3.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 3.75 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 3.75 m/sd = 200 mm
ṁ = kg/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.64h = 3.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 3.5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 3.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
4.Medium
d1​ = 100 mmd2​ = 60 mm12p1​ − p2​ = 35 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 60 mm. The pressure at the inlet is 35 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 60 mmp1 − p2 = 35 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 200 mm, p1​ = 220 kPad2​ = 75 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 7 m. At section 1 the pressure is 220 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 220 kPav1 = 0.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 120 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 2 m. At section 1 the pressure is 120 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 120 kPav1 = 3 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 6.188 m/s
  2. 2. ṁ = 103.7 kg/s
  3. 3. Q = 2.603 L/s
  4. 4. Q = 25.36 L/s
  5. 5. p2 = 145.1 kPa
  6. 6. p2 = 82.1 kPa

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