Chapter – 4

Computation of :-

A. Specific Energy

B. Specific Force

C. Critical Depth

Learning Objectives:-

•Specific energy and specific force

•Computation of critical depth and

hydraulic exponent

•Application of critical depth

INTRODUCTION

The concept of specific energy originally proposed byBakhmeteff [1] has lot of advantages in the analysisof open channel flow.

Specific energy , specific force and critical depth areintimately connected specially in the study of criticalflow of an open channel.

Critical depth has a lot application in the flowmeasuring device and to indicate the names ofgradually varied flow profiles and their computation.

A. SPECIFIC ENERGY

SPECIFIC ENERGY CURVE

CHARACTERISTICS OF THE CURVE

alternate depths.

MINIMUM SPECIFIC ENERGY AT A GIVEN DISCHARGE

MAXIMUM DISCHARGE AT A GIVEN SPECIFIC ENERGY

Which is Eq (3.3) and this equation represents the critical flow condition, i.e,for a given E and maximum Q, flow condition is critical

MOMENTUM EQUATION

B. SPECIFIC FORCE

SPECIFIC FORCE CURVE

The curve has two limbs, CA and CB. The limb CA approaches x-axisasymptotically. The limb CB rises upwards and extends indefinitely.For a given value of specific force, the curve has two depths at Y1

and Y2, i.e., F1 = F2 = F. It will be shown later that these two depthsare initial and sequent depths of hydraulic jump.

At point VC, the depths become one and corresponding specific forceis minimum. The depth of minimum specific force is called criticaldepth Yc. Corresponding specific force curves are drawn withincrease of discharge, i.e., Q1> Q, Q2 > Q1 and the line of minimumspecific force are drawn (EC C1 C2 F).

The region below this line is supercritical zone and above this line issubcritical zone. It shows that just like specific energy case, for agiven discharge for minimum specific for maximum discharge.

The above tow conditions may be worked analytically just like thecase of specific energy to arrive at the critical flow condition Q2T/gA3

=1.

C. CRITICAL DEPTH COMPUTATION

EXAMPLE

EXAMPLE

Solution: