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 = 40 mm, v = 3 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 3 m/sd = 40 mm
ṁ = kg/s
2.Easy
12d1​ = 200 mm, v1​ = 0.5 m/sd2​ = 40 mm

Water flows at 0.5 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 40 mmv1 = 0.5 m/s
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = 160 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 160 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 160 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 80 mmd2​ = 40 mm12p1​ − p2​ = 54 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 80 mm and a throat diameter of 40 mm. The pressure at the inlet is 54 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 80 mmd2 = 40 mmp1 − p2 = 54 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 370 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 8 m. At section 1 the pressure is 370 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 370 kPav1 = 2.25 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 50 mmp1​ = 110 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 110 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 = 110 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 4.75 kg/s
  2. 2. Q = 15.71 L/s
  3. 3. p2 = 144.6 kPa
  4. 4. Q = 13.49 L/s
  5. 5. p2 = 253.6 kPa
  6. 6. H = 12.88 m

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