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​ = 200 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 50 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12d = 25 mm, v = 1.5 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.5 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.5 m/sd = 25 mm
ṁ = kg/s
3.Medium
d1​ = 200 mmd2​ = 150 mm12p1​ − p2​ = 22 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 150 mm. The pressure at the inlet is 22 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 150 mmp1 − p2 = 22 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 260 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 260 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 260 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 280 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 280 mm. The discharge coefficient is 0.99. 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 = 280 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 220 kPad2​ = 50 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 4 m. At section 1 the pressure is 220 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 220 kPav1 = 0.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 8 m/s
  2. 2. ṁ = 0.9278 kg/s
  3. 3. Q = 141.8 L/s
  4. 4. p2 = 170 kPa
  5. 5. Q = 16.7 L/s
  6. 6. p2 = 180.3 kPa

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