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​ = 2.25 m/sd2​ = 50 mm

Water flows at 2.25 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 = 50 mmv1 = 2.25 m/s
Q = L/s
2.Easy
12d1​ = 100 mm, v1​ = 1.25 m/sd2​ = 50 mm

Water flows at 1.25 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 = 50 mmv1 = 1.25 m/s
Q = L/s
3.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 46 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 46 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 46 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
d1​ = 80 mmd2​ = 40 mm12p1​ − p2​ = 13 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 80 mm and a throat diameter of 40 mm. The pressure at the inlet is 13 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 80 mmd2 = 40 mmp1 − p2 = 13 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 200 mmd2​ = 100 mm12Δh = 390 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 390 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 = 200 mmd2 = 100 mmΔh = 390 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
H = ?d1​ = 50 mmp1​ = 100 kPad2​ = 30 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 50 mm and a gauge pressure of 100 kPa. The nozzle exit diameter is 30 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 50 mmp1 = 100 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 17.67 L/s
  2. 2. Q = 9.817 L/s
  3. 3. Q = 77.8 L/s
  4. 4. Q = 6.618 L/s
  5. 5. Q = 75.66 L/s
  6. 6. H = 11.71 m

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