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 = 40 mm, v = 2.25 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 2.25 m/sd = 40 mm
ṁ = kg/s
2.Easy
12d1​ = 100 mm, v1​ = 1.75 m/sd2​ = 40 mm

Water flows at 1.75 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 = 40 mmv1 = 1.75 m/s
Q = L/s
3.Medium
12d1​ = 75 mm, p1​ = 400 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 400 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 400 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 360 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 25 mm. In the wide section the pressure is 360 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 25 mmp1 = 360 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 320 kPad2​ = 75 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 9 m. At section 1 the pressure is 320 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 320 kPav1 = 0.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 150 mmd2​ = 75 mm12Δh = 230 mmmercuryQ = ?

A horizontal venturi meter (inlet 150 mm, throat 75 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 230 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 = 150 mmd2 = 75 mmΔh = 230 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 2.827 kg/s
  2. 2. Q = 13.74 L/s
  3. 3. p2 = 396.8 kPa
  4. 4. p2 = 288.3 kPa
  5. 5. p2 = 231.1 kPa
  6. 6. Q = 33.72 L/s

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