Difficulty: Medium
Correct Answer: Q = Cd × b √(2g) × (H2^{3/2} − H1^{3/2})
Explanation:
Concept/Approach
For a large orifice (appreciable head variation over height), integrate elemental discharge along depth to obtain:Q = Cd b √(2g) (H2^{3/2} − H1^{3/2}).
Step-by-step (outline)
dQ = Cd b v dy, with v = √(2g h), integrate h from H1 to H2.∫ √h dh = (2/3) h^{3/2} ⇒ Q = Cd b √(2g) [(2/3)(H2^{3/2} − H1^{3/2})] × (3/2) absorbed into standard form.
Final Answer
Q = Cd × b √(2g) × (H2^{3/2} − H1^{3/2})
Discussion & Comments