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​ = 75 mm, v1​ = 2.75 m/sd2​ = 40 mm

Water flows at 2.75 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 2.75 m/s
Q = L/s
2.Easy
vd = 40 mmh = 1 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 1 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 1 mg = 9.81 m/s²d = 40 mm
Q = L/s
3.Medium
12d1​ = 75 mm, p1​ = 320 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 320 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 320 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 20 mm, Cd​ = 0.6h = 1.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 1.5 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 1.5 mCd = 0.6g = 9.81 m/s²
Q = L/s
5.Hard
H = ?d1​ = 75 mmp1​ = 30 kPad2​ = 25 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 75 mm and a gauge pressure of 30 kPa. The nozzle exit diameter is 25 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 = 75 mmp1 = 30 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
pair​ = 150 kPaQ = ?d = 30 mmh = 4.5 m

A closed water tank has compressed air above the water at a gauge pressure of 150 kPa. Water leaves through an opening with a diameter of 30 mm, 4.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 150 kPa (gauge)h = 4.5 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 12.15 L/s
  2. 2. Q = 5.566 L/s
  3. 3. p2 = 316.8 kPa
  4. 4. Q = 1.023 L/s
  5. 5. H = 3.096 m
  6. 6. Q = 13.93 L/s

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