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
vd = 40 mmh = 6 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 6 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 6 mg = 9.81 m/s²d = 40 mm
Q = L/s
2.Easy
12d1​ = 100 mm, v1​ = 2 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 40 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 2 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 150 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 150 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 150 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 80 kPa

Water flows at 40 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 80 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 40 L/sd1 = 200 mmd2 = 100 mmp2 = 80 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
C211 m2.5 md = 50 mmQ = ?

A hose with an inner diameter of 50 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 2.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 50 mmzC = +1 mz2 = −2.5 mg = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 30 kPaQ = ?d = 40 mmh = 2 m

A closed water tank has compressed air above the water at a gauge pressure of 30 kPa. Water leaves through an opening with a diameter of 40 mm, 2 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 30 kPa (gauge)h = 2 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 13.63 L/s
  2. 2. v2 = 12.5 m/s
  3. 3. p2 = 148.9 kPa
  4. 4. p1 = 92.16 kPa
  5. 5. Q = 13.75 L/s
  6. 6. Q = 12.52 L/s

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