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
v = ?h = 3.5 m

An open water tank drains through a small opening in its side. The free surface is 3.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 3.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1.5 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 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 1.5 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 27 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 27 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 27 kPaρ = 1000 kg/m³
v = m/s
4.Medium
d1​ = 250 mmd2​ = 125 mm12p1​ − p2​ = 6 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 250 mm and a throat diameter of 125 mm. The pressure at the inlet is 6 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 250 mmd2 = 125 mmp1 − p2 = 6 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
C211.5 m4 md = 20 mmpC​ = ?

A hose with an inner diameter of 20 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 4 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 = 20 mmzC = +1.5 mz2 = −4 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
C211.5 m1.5 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 1.5 m above the water surface, and the outlet (open to the air) is 1.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 50 mmzC = +1.5 mz2 = −1.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v = 8.287 m/s
  2. 2. v2 = 6 m/s
  3. 3. v = 7.348 m/s
  4. 4. Q = 43.91 L/s
  5. 5. pC = 47.34 kPa
  6. 6. Q = 10.65 L/s

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