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
12d1​ = 100 mm, v1​ = 2 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 2 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1.5 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 1.5 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 7 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 7 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 7 kPaρ = 1000 kg/m³
v = m/s
4.Medium
Q = ?d = 50 mm, Cd​ = 0.65h = 6 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 6 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 6 mCd = 0.65g = 9.81 m/s²
Q = L/s
5.Hard
C213 m4.5 md = 40 mmpC​ = ?

A hose with an inner diameter of 40 mm siphons water from an open tank. The highest point C of the hose is 3 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 absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 40 mmzC = +3 mz2 = −4.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.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

Answer key

  1. 1. v2 = 8 m/s
  2. 2. v2 = 2.667 m/s
  3. 3. v = 3.742 m/s
  4. 4. Q = 13.85 L/s
  5. 5. pC = 27.72 kPa
  6. 6. H = 7.172 m

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