Effect of Viscosity on Orifice (Hole) Discharge The viscosity of a liquid ______ its rate of flow through a small hole (orifice) in a vessel under gravity.

Introduction:
Real fluids experience internal friction (viscosity). When discharging through an orifice, viscous shear and boundary effects reduce the actual flow rate compared to the ideal inviscid prediction.

Given Data / Assumptions:

• Small to moderate orifice, sharp-edged opening.
• Gravity-driven discharge from a tank.
• Steady conditions; no aeration or cavitation.

Concept / Approach:
Ideal discharge is given by Torricelli's formula Q_ideal = A * sqrt(2gh). Real discharge is Q = C_d * A * sqrt(2gh), where C_d (coefficient of discharge) accounts for contraction and viscosity. Higher viscosity reduces C_d and therefore reduces Q.

Step-by-Step Solution:
Start with Q = C_d * A * sqrt(2gh).As viscosity increases, energy losses rise and C_d decreases.Hence, for the same head h and area A, Q decreases.

Verification / Alternative check:
Compare water and glycerin under equal head: measured flow of glycerin is far smaller because its dynamic viscosity is orders of magnitude higher, confirming the decrease.

Why Other Options Are Wrong:
Increase: contradicts energy loss physics.
No effect: true only in the inviscid idealization, which ignores real losses.
First increases then decreases: not observed for ordinary ranges in simple orifices; monotonic reduction is typical as viscosity rises.

Common Pitfalls:
Using ideal Torricelli without discharge coefficients; ignoring temperature dependence of viscosity; misreading head levels causing apparent anomalies.

Final Answer:
decreases the rate of flow