Q1: The discharge through a V-notch weir varies as

ANS:D - H^7/2

Apologies for the confusion. It seems there was an error in the initial response. The discharge through a V-notch weir typically varies as 5/2H5/2, not 7/2H7/2. Here's a brief explanation: In the context of a V-notch weir, the discharge Q is often expressed as a function of the head H of water over the notch. The general formula for the discharge Q through a V-notch weir is given by: 5/2Q=C×H5/2 Where:

• Q is the discharge rate,
• C is a constant that depends on the geometry of the V-notch and other factors,
• H is the head of water over the notch.

This formula is derived from theoretical and experimental analyses of fluid flow over the weir crest. The exponent 5/25/2 arises from the mathematics of fluid flow through a V-notch, and it represents the relationship between the discharge and the head of water. Therefore, 5/2H5/2 is the correct term to describe the variation of discharge through a V-notch weir, not 7/2H7/2. Thank you for your patience, and I apologize for any confusion caused by the earlier response.