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
vd = 10 mmh = 4 m

An open water tank drains through a round opening with a diameter of 10 mm in its side. The free surface is 4 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 4 mg = 9.81 m/s²d = 10 mm
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 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 = 75 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
3.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 26 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 50 mm. The pressure at the inlet is 26 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 26 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 380 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 380 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 380 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 40 kPav = ?d = 40 mmh = 3 m

A closed water tank has compressed air above the water at a gauge pressure of 40 kPa. Water leaves through an opening with a diameter of 40 mm, 3 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 40 kPa (gauge)h = 3 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 150 mm, p1​ = 300 kPad2​ = 100 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 9 m. At section 1 the pressure is 300 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 300 kPav1 = 2.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 0.6958 L/s
  2. 2. v2 = 1.125 m/s
  3. 3. Q = 14.62 L/s
  4. 4. p2 = 317.5 kPa
  5. 5. v = 11.78 m/s
  6. 6. p2 = 196.3 kPa

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