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
v = ?h = 5 m

An open water tank drains through a small opening in its side. The free surface is 5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 150 mm, v1​ = 2.5 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 2.5 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 2.5 m/s
v2 = m/s
3.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 24 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 300 mm and a throat diameter of 150 mm. The pressure at the inlet is 24 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 24 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 150 mm, p1​ = 250 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 250 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 250 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
H = ?d1​ = 75 mmp1​ = 70 kPad2​ = 20 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 70 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 = 75 mmp1 = 70 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 100 mm, p1​ = 400 kPad2​ = 40 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 6 m. At section 1 the pressure is 400 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 400 kPav1 = 1.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 9.905 m/s
  2. 2. v2 = 5.625 m/s
  3. 3. Q = 126.4 L/s
  4. 4. p2 = 239.7 kPa
  5. 5. H = 7.172 m
  6. 6. p2 = 282.9 kPa

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