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​ = 150 mm, v1​ = 2 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 2 m/s
v2 = m/s
2.Easy
12d = 100 mm, v = 2.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 2.25 m/sd = 100 mm
ṁ = kg/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.65h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 1 mCd = 0.65g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 1150 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1150 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1150 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 270 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 1 m. At section 1 the pressure is 270 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 270 kPav1 = 2.75 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 140 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 140 mm. The discharge coefficient is 0.97. 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 = 140 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 4.5 m/s
  2. 2. ṁ = 22.27 kg/s
  3. 3. Q = 0.9045 L/s
  4. 4. v = 43.78 m/s
  5. 5. p2 = 203.5 kPa
  6. 6. Q = 17.29 L/s

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