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 = 200 mm, v = 2.5 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 2.5 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 2.5 m/sd = 200 mm
ṁ = kg/s
2.Easy
12d = 200 mm, v = 1 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 1 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 1 m/sd = 200 mm
ṁ = kg/s
3.Medium
12d1​ = 150 mm, p1​ = 190 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 190 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 190 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 140 kPa

Water flows at 6 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 140 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 6 L/sd1 = 150 mmd2 = 75 mmp2 = 140 kPaρ = 1000 kg/m³
p1 = kPa
5.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 0.96. 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 = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 8 m. At section 1 the pressure is 280 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 280 kPav1 = 2.25 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 80.5 kg/s
  2. 2. ṁ = 32.2 kg/s
  3. 3. p2 = 143.1 kPa
  4. 4. p1 = 140.9 kPa
  5. 5. Q = 17.12 L/s
  6. 6. p2 = 191.2 kPa

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