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
12d = 150 mm, v = 3.75 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 3.75 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 3.75 m/sd = 150 mm
ṁ = kg/s
3.Medium
12d1​ = 100 mm, p1​ = 170 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 170 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 170 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 300 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 300 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 300 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 380 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 4 m. At section 1 the pressure is 380 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 380 kPav1 = 2 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 60 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 60 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 = 80 mmd2 = 40 mmΔh = 60 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. ṁ = 83.5 kg/s
  3. 3. p2 = 123.1 kPa
  4. 4. p2 = 253.1 kPa
  5. 5. p2 = 310.8 kPa
  6. 6. Q = 4.898 L/s

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