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
12Q = 57 L/sv = 3 m/s, d = ?

A water line must carry 57 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 57 L/sv = 3 m/s
d = mm
2.Easy
12d = 80 mm, v = 0.5 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 0.5 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 0.5 m/sd = 80 mm
ṁ = kg/s
3.Medium
12d1​ = 150 mm, p1​ = 280 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 280 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 280 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 350 Paρ = 1.2 kg/m³
v = m/s
5.Hard
H = ?d1​ = 75 mmp1​ = 150 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 150 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 = 150 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 150 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 6 m. At section 1 the pressure is 280 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 280 kPav1 = 1.25 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 155.5 mm
  2. 2. ṁ = 3.167 kg/s
  3. 3. p2 = 273.8 kPa
  4. 4. v = 24.15 m/s
  5. 5. H = 15.37 m
  6. 6. p2 = 158.6 kPa

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