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 = 200 mm, v = 2.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 2.25 m/sd = 200 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 1.5 m/sd2​ = 50 mm

Water flows at 1.5 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 = 50 mmv1 = 1.5 m/s
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 380 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 380 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 380 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 370 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 370 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 370 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 70 kPav = ?d = 25 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 25 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 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
H = ?d1​ = 100 mmp1​ = 120 kPad2​ = 25 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 120 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 = 100 mmp1 = 120 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 89.06 kg/s
  2. 2. Q = 6.627 L/s
  3. 3. p2 = 368.3 kPa
  4. 4. p2 = 363.8 kPa
  5. 5. v = 13.75 m/s
  6. 6. H = 12.28 m

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