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​ = 75 mm, v1​ = 1.5 m/sd2​ = 40 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 1.5 m/s
Q = L/s
2.Easy
12Q = 10 L/sv = 2 m/s, d = ?

A water line must carry 10 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 10 L/sv = 2 m/s
d = mm
3.Medium
Q = ?d = 40 mm, Cd​ = 0.62h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.62. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 1 mCd = 0.62g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 700 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 700 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 700 Paρ = 1.2 kg/m³
v = m/s
5.Hard
H = ?d1​ = 100 mmp1​ = 50 kPad2​ = 30 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 50 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 = 100 mmp1 = 50 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
C211.5 m3.5 md = 25 mmQ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 1.5 m above the water surface, and the outlet (open to the air) is 3.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 25 mmzC = +1.5 mz2 = −3.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 6.627 L/s
  2. 2. d = 79.79 mm
  3. 3. Q = 3.451 L/s
  4. 4. v = 34.16 m/s
  5. 5. H = 5.138 m
  6. 6. Q = 4.068 L/s

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