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
12d = 100 mm, v = 1.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1.75 m/sd = 100 mm
ṁ = kg/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
d1​ = 200 mmd2​ = 150 mm12p1​ − p2​ = 30 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 150 mm. The pressure at the inlet is 30 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 150 mmp1 − p2 = 30 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
Q = ?d = 40 mm, Cd​ = 0.64h = 3.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 3.5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 3.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
H = ?d1​ = 50 mmp1​ = 150 kPad2​ = 20 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 150 kPa. The nozzle exit diameter is 20 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 = 150 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
pair​ = 200 kPaQ = ?d = 50 mmh = 2.5 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 50 mm, 2.5 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 = 2.5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 12.1 kg/s
  2. 2. Q = 11.78 L/s
  3. 3. Q = 165.6 L/s
  4. 4. Q = 6.665 L/s
  5. 5. H = 15.69 m
  6. 6. Q = 41.61 L/s

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