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​ = 150 mm, v1​ = 2 m/sd2​ = 75 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 2 m/s
Q = L/s
2.Easy
12Q = 50 L/sv = 1.5 m/s, d = ?

A water line must carry 50 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 50 L/sv = 1.5 m/s
d = mm
3.Medium
d1​ = 250 mmd2​ = 125 mm12p1​ − p2​ = 6 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 250 mm and a throat diameter of 125 mm. The pressure at the inlet is 6 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 250 mmd2 = 125 mmp1 − p2 = 6 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 240 kPa

Water flows at 25 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 240 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 25 L/sd1 = 200 mmd2 = 100 mmp2 = 240 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
d1​ = 150 mmd2​ = 100 mm12Δh = 270 mmmercuryQ = ?

A horizontal venturi meter (inlet 150 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 270 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 = 150 mmd2 = 100 mmΔh = 270 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 70 kPav = ?d = 50 mmh = 2.5 m

A closed water tank has compressed air above the water at a gauge pressure of 70 kPa. Water leaves through an opening with a diameter of 50 mm, 2.5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 70 kPa (gauge)h = 2.5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. Q = 35.34 L/s
  2. 2. d = 206 mm
  3. 3. Q = 43.91 L/s
  4. 4. p1 = 244.7 kPa
  5. 5. Q = 68.05 L/s
  6. 6. v = 13.75 m/s

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