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​ = 0.75 m/sd2​ = 75 mm

Water flows at 0.75 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 = 0.75 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 100 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 100 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 100 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.61h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 4 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 4 mCd = 0.61g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 160 kPad2​ = 25 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 6 m. At section 1 the pressure is 160 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 160 kPav1 = 1.25 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 360 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 360 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 = 50 mmΔh = 360 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 5.89 L/s
  2. 2. v2 = 4.395 m/s
  3. 3. p2 = 90 kPa
  4. 4. Q = 2.653 L/s
  5. 5. p2 = 38.64 kPa
  6. 6. Q = 18.56 L/s

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