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​ = 75 mm, v1​ = 2.25 m/sd2​ = 40 mm

Water flows at 2.25 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 2.25 m/s
Q = L/s
2.Easy
vd = 30 mmh = 3 m

An open water tank drains through a round opening with a diameter of 30 mm in its side. The free surface is 3 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 3 mg = 9.81 m/s²d = 30 mm
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 220 kPa

Water flows at 27 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 220 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 27 L/sd1 = 100 mmd2 = 75 mmp2 = 220 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
Q = ?d = 50 mm, Cd​ = 0.64h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 1 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 190 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 5 m. At section 1 the pressure is 190 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 190 kPav1 = 2 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 200 mmd2​ = 150 mm12Δh = 390 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 390 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 = 200 mmd2 = 150 mmΔh = 390 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 9.94 L/s
  2. 2. Q = 5.423 L/s
  3. 3. p1 = 232.8 kPa
  4. 4. Q = 5.566 L/s
  5. 5. p2 = 136.6 kPa
  6. 6. Q = 199.4 L/s

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