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​ = 0.5 m/sd2​ = 50 mm

Water flows at 0.5 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 = 50 mmv1 = 0.5 m/s
Q = L/s
2.Easy
12d = 40 mm, v = 1.25 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1.25 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1.25 m/sd = 40 mm
ṁ = kg/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.61h = 4.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 4.5 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 = 4.5 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 190 kPa

Water flows at 22 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 190 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 22 L/sd1 = 150 mmd2 = 75 mmp2 = 190 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
d1​ = 250 mmd2​ = 125 mm12Δh = 240 mmmercuryQ = ?

A horizontal venturi meter (inlet 250 mm, throat 125 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 240 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 = 250 mmd2 = 125 mmΔh = 240 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 90 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 90 mm. The discharge coefficient is 0.95. 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 = 90 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 3.927 L/s
  2. 2. ṁ = 1.382 kg/s
  3. 3. Q = 2.814 L/s
  4. 4. p1 = 201.6 kPa
  5. 5. Q = 95.67 L/s
  6. 6. Q = 9.087 L/s

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