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​ = 100 mm, v1​ = 1.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 1.5 m/s
v2 = m/s
2.Easy
12d = 150 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 150 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 2.75 m/sd = 150 mm
ṁ = kg/s
3.Medium
v = ?p0​pp0​ − p = 1350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1350 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 260 kPa

Water flows at 32 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 260 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 32 L/sd1 = 150 mmd2 = 75 mmp2 = 260 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 280 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 200 mm to 40 mm while rising 1 m. At section 1 the pressure is 280 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 40 mmp1 = 280 kPav1 = 0.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 300 mmd2​ = 150 mm12Δh = 180 mmmercuryQ = ?

A horizontal venturi meter (inlet 300 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 180 mm. The discharge coefficient is 0.98. 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 = 300 mmd2 = 150 mmΔh = 180 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 6 m/s
  2. 2. ṁ = 48.6 kg/s
  3. 3. v = 47.43 m/s
  4. 4. p1 = 284.6 kPa
  5. 5. p2 = 192.2 kPa
  6. 6. Q = 119.3 L/s

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