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 = 3.75 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 3.75 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 3.75 m/sd = 50 mm
ṁ = kg/s
2.Easy
vd = 10 mmh = 4.5 m

An open water tank drains through a round opening with a diameter of 10 mm in its side. The free surface is 4.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 4.5 mg = 9.81 m/s²d = 10 mm
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 850 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 850 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 850 Paρ = 1.2 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 11 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 11 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 11 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 280 kPad2​ = 75 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 3 m. At section 1 the pressure is 280 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 280 kPav1 = 1.75 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 120 kPaQ = ?d = 50 mmh = 3.5 m

A closed water tank has compressed air above the water at a gauge pressure of 120 kPa. Water leaves through an opening with a diameter of 50 mm, 3.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 120 kPa (gauge)h = 3.5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 7.547 kg/s
  2. 2. Q = 0.738 L/s
  3. 3. v = 37.64 m/s
  4. 4. v = 4.69 m/s
  5. 5. p2 = 247.3 kPa
  6. 6. Q = 34.5 L/s

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