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​ = 1.25 m/sd2​ = 75 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 75 mmv1 = 1.25 m/s
Q = L/s
2.Easy
12d = 100 mm, v = 1 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 1 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 1 m/sd = 100 mm
ṁ = kg/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.65h = 3 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 3 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 3 mCd = 0.65g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 250 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 250 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 250 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 230 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 1 m. At section 1 the pressure is 230 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 230 kPav1 = 1 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 160 mmmercuryQ = ?

A horizontal venturi meter (inlet 80 mm, throat 40 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 160 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 = 80 mmd2 = 40 mmΔh = 160 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 9.817 L/s
  2. 2. ṁ = 7.854 kg/s
  3. 3. Q = 2.448 L/s
  4. 4. v = 20.41 m/s
  5. 5. p2 = 201.2 kPa
  6. 6. Q = 7.754 L/s

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