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 = 40 mm, v = 2.75 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 2.75 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 2.75 m/sd = 40 mm
ṁ = kg/s
2.Easy
12d1​ = 200 mm, v1​ = 1.5 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 1.5 m/s
v2 = m/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.64h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 4 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 4 mCd = 0.64g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 1000 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1000 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1000 Paρ = 1.2 kg/m³
v = m/s
5.Hard
pair​ = 190 kPav = ?d = 40 mmh = 1 m

A closed water tank has compressed air above the water at a gauge pressure of 190 kPa. Water leaves through an opening with a diameter of 40 mm, 1 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 190 kPa (gauge)h = 1 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 150 mm, p1​ = 130 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 2 m. At section 1 the pressure is 130 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 130 kPav1 = 0.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 3.456 kg/s
  2. 2. v2 = 10.67 m/s
  3. 3. Q = 1.781 L/s
  4. 4. v = 40.82 m/s
  5. 5. v = 19.99 m/s
  6. 6. p2 = 87.88 kPa

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