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 = 150 mm, v = 0.5 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 0.5 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 0.5 m/sd = 150 mm
ṁ = kg/s
2.Easy
vd = 10 mmh = 3 m

An open water tank drains through a round opening with a diameter of 10 mm in its side. The free surface is 3 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 3 mg = 9.81 m/s²d = 10 mm
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = 350 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 350 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 350 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
4.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 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 320 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
H = ?d1​ = 50 mmp1​ = 70 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 70 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 = 70 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
H = ?d1​ = 75 mmp1​ = 20 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 20 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 = 20 kPa (gauge)d2 = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 8.836 kg/s
  2. 2. Q = 0.6026 L/s
  3. 3. p2 = 345.4 kPa
  4. 4. p2 = 318.9 kPa
  5. 5. H = 8.198 m
  6. 6. H = 2.064 m

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