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 = 15 mmh = 3 m

An open water tank drains through a round opening with a diameter of 15 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 = 15 mm
Q = L/s
2.Easy
v = ?h = 7.5 m

An open water tank drains through a small opening in its side. The free surface is 7.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 7.5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 150 mm, p1​ = 340 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 340 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 340 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 26 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 26 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 26 kPaρ = 1000 kg/m³
v = m/s
5.Hard
d1​ = 300 mmd2​ = 150 mm12Δh = 280 mmmercuryQ = ?

A horizontal venturi meter (inlet 300 mm, throat 150 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 0.98. 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 = 300 mmd2 = 150 mmΔh = 280 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 170 kPaQ = ?d = 20 mmh = 1.5 m

A closed water tank has compressed air above the water at a gauge pressure of 170 kPa. Water leaves through an opening with a diameter of 20 mm, 1.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 170 kPa (gauge)h = 1.5 md = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 1.356 L/s
  2. 2. v = 12.13 m/s
  3. 3. p2 = 293.1 kPa
  4. 4. v = 7.211 m/s
  5. 5. Q = 148.8 L/s
  6. 6. Q = 6.038 L/s

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