**6.1 Paleodischarge (Qw)**

Channel dimensions and paleoslope along with flow velocity permit paleo channel reconstruction using bankfull channel width derived from regression equations and Gibling's scaling factor so as to account variability in channel cross sectional area due to depositional environment as used [6, 42]. A more robust method of estimating paleo-discharge is based on Bagnold's continuity equation as:

$$\mathbf{Q\_w} = \mathbf{V\_c} \mathbf{A} \tag{30}$$

$$\mathbf{Q\_w} = \mathbf{W\_c} \, \mathbf{D\_c} \mathbf{V\_c} \tag{31}$$

Where Qw is the discharge and A is the cross-sectional area, which is the product of channel bankfull width (Wc) and channel depth (Dc). Vc is paleoflow velocity was estimated by bedform phase diagram and Darcy Weisbach friction coefficient equation to estimate flow velocity under the assumption that the dominant bedform reflects dominant bed load transport condition during flooding event as described elsewhere. Given bankfull width (Wc), bankfull depth (Dc) and Vc = average flow velocity, Eq. (30) yields a calculated paleo-discharge of 22,070 m3 for Brahmini sub basin, 12,865 m3 for Pachwara, 5880 m3 for Chuperbhita and 4510 m3 for Hurra sub basin (**Table 1**).

Ref. [43] Related bankfull channel width (Wc) and maximum flow depth (Dc) to bankfull discharge defined as Q2.33 based on data collected by ref. [44] for semiarid and sub-humid stable alluvial channels in USA and Australia:

$$\mathbf{Q\_{2.33}} = 2.66 \,\mathrm{W\_c}^{0.9} \,\mathrm{D\_c}^{0.68} \tag{32}$$

On the other hand [45] demonstrate that peak annual flood fluvial discharge is related to drainage basin area (DA) by the equation:

$$\text{Log Q}\_{\text{flood}} = 2.084 - 0.070 \text{ log D}\_{\text{A}}^2 + 0.865 \text{ log D}\_{\text{A}} \tag{33}$$

Where Q flood is the discharge with a recurrence interval of 2.33 years and DA is the drainage basin area. Using previously estimates of (DA) in this Eq. (33) the mean annual *Analyzing Sedimentary Rocks to Evaluate Paleo Dimensions and Flow Dynamics of Permian… DOI: http://dx.doi.org/10.5772/intechopen.106994*

flood is estimated to be about 170,600 m3 /sec for Brahmini sub basin, 112,200 m3 /sec for Pachwara sub basin, 65,460 m3 /sec for Chuperbhita sub basin and 48,640 m3 /sec for Hurra sub basin of Rajmahal Gondwana basin, although there is an order of magnitude uncertainty in this calculation. It is emphasized that this value would not apply year round, would primarily reflect only times of high seasonal yearly discharge. Ref. [45] suggest on the basis of data compiled by them that Qflood/Qaverage ratios can range over 4 orders of magnitude, from 10 to 10,000. If this is correct than this ratio suggests that average discharge for Barakar Rivers could be as high as 17,060 m3 /sec but as low as 17 m3 /sec. It appears to be that the estimated average discharge of Barakar River compares well with the average discharge of many Indian continental rivers, for example Tapti (6317 m3 /sec), Godavari (3505 m3 /sec), and Indus (6600 m3 /sec).

Ref. [44] used regional hydraulic geometry curves to estimate the discharge of a number of ancient river system based on drainage area. These relationships are developed from analysis of rivers from different climatic and tectonics area. Ref. [4] point out that application to an ancient river system requires some knowledge of the climatic conditions prevailing at that time. The data for this approach require estimates of bankfull channel depth, which can be estimated from empirical relationship as outlined above. Ref. [44] provide hydraulic geometry curves derived using power-law relationships of the form:

$$\mathbf{D}\_{\mathbf{A}} = \mathbf{a} \, \mathbf{A}^{\mathbf{b}} \tag{34}$$

$$\mathbf{Q\_w} = \mathbf{a} \, \mathbf{A^b} \tag{35}$$

Combining Eqs. (33) and (34) we have

$$\mathbf{D}\_{\mathbf{A}} = \mathbf{Q}\_{\mathbf{w}} \tag{36}$$

The Eq. (36) strengthen the views expressed by several workers that in humid and semi-humid regions that area of the drainage basin is approximately equal to the mean annual discharge(Qw) as recently suggested by workers quoted above. If this is true of the Barakar river system of the study area, the drainage area was about 22,070 km<sup>2</sup> to 4510 km<sup>2</sup> . This relationship was used in an attempt to estimate paleoflow parameters of the streams in different parts of world [5, 46, 47].
