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​ = 1.25 m/sd2​ = 40 mm

Water flows at 1.25 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 = 1.25 m/s
Q = L/s
2.Easy
12d1​ = 100 mm, v1​ = 2 m/sd2​ = 75 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 75 mmv1 = 2 m/s
Q = L/s
3.Medium
Q = ?d = 30 mm, Cd​ = 0.62h = 3.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 3.5 m above the orifice and the discharge coefficient is 0.62. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 3.5 mCd = 0.62g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 170 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 170 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 170 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C211 m5 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 1 m above the water surface, and the outlet (open to the air) is 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 = +1 mz2 = −5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
H = ?d1​ = 75 mmp1​ = 140 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 140 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 = 140 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 5.522 L/s
  2. 2. Q = 15.71 L/s
  3. 3. Q = 3.632 L/s
  4. 4. p2 = 154.6 kPa
  5. 5. pC = 42.44 kPa
  6. 6. H = 14.34 m

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