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​ = 200 mm, v1​ = 1.25 m/sd2​ = 100 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 1.25 m/s
Q = L/s
2.Easy
12d1​ = 100 mm, v1​ = 1.5 m/sd2​ = 75 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 75 mmv1 = 1.5 m/s
Q = L/s
3.Medium
Q = ?d = 40 mm, Cd​ = 0.6h = 5.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 5.5 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 5.5 mCd = 0.6g = 9.81 m/s²
Q = L/s
4.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 38 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 300 mm and a throat diameter of 150 mm. The pressure at the inlet is 38 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 38 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 370 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 370 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 = 100 mmd2 = 50 mmΔh = 370 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 130 kPaQ = ?d = 40 mmh = 3.5 m

A closed water tank has compressed air above the water at a gauge pressure of 130 kPa. Water leaves through an opening with a diameter of 40 mm, 3.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 130 kPa (gauge)h = 3.5 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 39.27 L/s
  2. 2. Q = 11.78 L/s
  3. 3. Q = 7.832 L/s
  4. 4. Q = 159.1 L/s
  5. 5. Q = 18.42 L/s
  6. 6. Q = 22.78 L/s

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