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​ = 2.75 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 2.75 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 2.75 m/s
v2 = m/s
2.Easy
vd = 20 mmh = 2.5 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 2.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2.5 mg = 9.81 m/s²d = 20 mm
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 130 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 130 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 130 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 200 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 200 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 200 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 250 mmd2​ = 125 mm12Δh = 250 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 250 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 = 250 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 200 kPaQ = ?d = 30 mmh = 3 m

A closed water tank has compressed air above the water at a gauge pressure of 200 kPa. Water leaves through an opening with a diameter of 30 mm, 3 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 200 kPa (gauge)h = 3 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 4.889 m/s
  2. 2. Q = 2.2 L/s
  3. 3. p2 = 100 kPa
  4. 4. p2 = 124.1 kPa
  5. 5. Q = 97.65 L/s
  6. 6. Q = 15.14 L/s

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