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 = 100 mm, v = 2.5 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2.5 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2.5 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 200 mm, v1​ = 1 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 1 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 290 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 290 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 290 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 310 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 50 mm. In the wide section the pressure is 310 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 310 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C210.5 m4.5 md = 32 mmQ = ?

A hose with an inner diameter of 32 mm siphons water from an open tank. The highest point C of the hose is 0.5 m above the water surface, and the outlet (open to the air) is 4.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 32 mmzC = +0.5 mz2 = −4.5 mg = 9.81 m/s²
Q = L/s
6.Hard
H = ?d1​ = 75 mmp1​ = 30 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 30 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 = 30 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. ṁ = 17.28 kg/s
  2. 2. v2 = 7.111 m/s
  3. 3. p2 = 238.9 kPa
  4. 4. p2 = 270 kPa
  5. 5. Q = 7.557 L/s
  6. 6. H = 3.074 m

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