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 = 100 mm, v = 3 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 3 m/sd = 100 mm
ṁ = kg/s
2.Easy
12Q = 22 L/sv = 3 m/s, d = ?

A water line must carry 22 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 22 L/sv = 3 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 300 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 300 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 300 Paρ = 1.2 kg/m³
v = m/s
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 56 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 56 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 56 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 250 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 60 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 250 mm. The discharge coefficient is 0.95. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 100 mmd2 = 60 mmΔh = 250 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 100 mm, p1​ = 140 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 140 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 140 kPav1 = 0.5 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 23.56 kg/s
  2. 2. d = 96.63 mm
  3. 3. v = 22.36 m/s
  4. 4. Q = 85.84 L/s
  5. 5. Q = 22.63 L/s
  6. 6. p2 = 120.1 kPa

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