The law of Newtonian viscosity is derived and the suite of continuum equations controlling the mechanics of fluids presented. Conditions for viscous flow to be considered incompressible are derived and the Navier–Stokes equations defined. Dimensional analysis is described along with the idea of similarity of two flow fields occurring on different spatial and temporal scales. The nature of the boundary and initial conditions for a flow domain are obtained that result in unique solutions of the linear form of the Navier–Stokes equations along with the specific boundary conditions on the flow fields that hold at fluid–solid and fluid–fluid interfaces. Analytical solutions of viscous flow are obtained for a range a specific, and simple, steady-state flow geometries. Time harmonic flow in straight conduits is determined as is the magnetohydrodynamic flow taking place in straight conduits filled with an electrically conducting fluid and a magnetic field applied perpendicularly to the conduit. In the guided exercises, the lubrication approximation is used to obtain approximate solutions for a range of flow scenarios.

With a legacy of sociopolitical and economic exclusion, ethnic conflicts, and an extremely arid climate, the Turkana people struggle to meet the two most basic necessities of life – food and water. One perennial river flowing from Uganda replenishes the groundwater on which the survival and growth of Lodwar depends. Lodwar’s water utility ranks poorly across national regulation metrics delivering an average of 24 litres per person per day to half of the town’s residents. Violent flash floods are known to wash away homes, people and animals almost every year. Relocating to safer grounds in peri-urban areas means losing income opportunities, education and healthcare services, and most importantly, water. A vibrant informal market has emerged, with tanker trucks and motorbikes selling water from the utility’s boreholes at high costs. For those who cannot afford vended water, scooping out dry riverbeds is the only option. With the discovery of crude oil and untapped groundwater reserves, coupled with construction of regional transport links, there is optimism for economic development in this marginalised county. Yet unless there is action to address the fundamental lack of capacity or coordination among multiple stakeholders, Lodwar’s water woes are likely to limit human and economic development.

Dhaka’s rivers are severely polluted by daily discharge of untreated industrial wastewater, coupled with raw sewage, and solid wastes from the city’s 20 million residents. The ready-made garment industry, a key player in the country’s economic growth since the 1990s, significantly contributes to this environmental degradation which disproportionately affects low-income riverbank communities, who rely on the contaminated water for daily activities. We explore these social inequalities through observation of people’s river use behaviour across the dry and wet seasons. In densely populated slums, women and girls turn to the rivers for washing clothes and dishes to avoid long queues at shared water points. Meanwhile, men engage in washing and bathing near bustling marketplaces and boat terminals. During the monsoon, recreational activities like swimming and fishing increase, as the rising water levels create a deceptive appearance of cleanliness. Supported by monthly river quality monitoring, household surveys, and regulatory analysis, these ‘river diaries’ paint the complexities of water-society dynamics. Findings identify priority responses for the most vulnerable today with analysis to guide the sequencing and prioritisation of major investments in water treatment infrastructure in the coming decades.

An in-depth and personal view of removal and homesteading in Colorado, through the experience of the Ute Tribes and Ferry Carpenter, ranch owner, and the first director of the Federal Grazing Service.

Despite the contrasts in history and hydroclimatic contexts, the water diaries of Bangladeshis and Kenyans reveal similar daily practices. Rains stand out as the most defining driver of water source choice. Rural populations in Khulna and Kitui shift to rainwater when available, whether harvested in containers from their own roof catchments or in rocks and dams. Whether in sarees or sarongs, in kolshis stacked on the waist or jerrycans balanced on the head, women are the primary drawers of water. When water needs to be transported via motorcycles or boats, a well is dug or a community tube well is installed, men come onto the scene. Individual practices are shaped by institutional behaviours and the quality of water governance. Regulation is missing or ineffective for rural drinking water services in Kitui and Khulna, while non-compliance is normalised in case of urban water pollution in Dhaka and unreliable piped supply in Lodwar. Our findings propose that policy and practice focus more attention on the interactions between rainfall and water use behaviours in a changing climate, and the need for better information on water risks for institutional accountability and sustainable finance. We finally chart where change is happening to improve water security in Bangladesh and the opportunities that exist in Kenya.

Explains Doctrine of Discovery as foundation for land divestiture that allowed non-Indigenous ranchers to acquire title to vast areas of Tribal land in 1800s and 1900s.

This chapter examines the opportunities and challenges for the management of biodiversity in desert and water-scarce regions, in particular sub-regions of the Middle East and North Africa (MENA) region. It explores the need for the integrated management of water and biodiversity in the region, how the current legal framework of biodiversity protection can advance an integrated governance approach, the gaps in integrative governance in the region, and how these gaps can be addressed. Although MENA is one of the regions most vulnerable to climate change, it is not homogenous. Its geography deserves a nuanced investigation of the threats of climate change and biodiversity loss to each of its sub-regions. The integrated management of water and biodiversity resources is essential to address the impacts of climate change and other ecological pressures coherently. To advance such integrated governance of water and biodiversity, a wide array of cross-sub regional and cross-national initiatives have been developed. However, problems of diverse political landscape, economic priorities, varied institutional capacities, and transboundary challenges hinder their effective and coherent implementation. This chapter examines the legal framework on the integrated management of water and biodiversity in the MENA region, offering recommendations for improving the current regime of water conservation.

This chapter examines the international legal framework on biodiversity, reflects on the scope of its implementation in the Middle East and North Africa (MENA) region, and highlights the way forward for enhancing coherent, holistic, and integrated implementation of biodiversity treaties in the region. It provides an overview of the status of implementation, primarily through an assessment of the progress of the Strategic Plan for Biodiversity including the Aichi targets (2011–2020), under the Convention of Biological Diversity, and assesses the challenges and opportunities of the post-2020 Global Biodiversity Framework. In addition to a literature review, the chapter analyses information from national reports by parties submitted to secretariats to the CBD and on informational platforms such as UNEP’s InforMEA and Law and Environment Assistance Platform.

In this chapter, the student learns how to perform certain classes of definite integrals using contour integration methods. Although the integration variable is real for most integrals of interest, such as the inverse Fourier transform, analysis of the integral is extended to complex values of the integration variable and theorems related to integrating around closed contours on the complex plane are used to solve classes of definite integrals. The key theorems include Cauchy’s theorem for integrating so-called analytic functions, Jordan’s lemma, and the residue theorem for the important case where inside a closed contour on the complex plane, the integrand has places called singularities at which the function is not well behaved. Contour integration is used to analyze and derive results for the constitutive laws of a material when the current response depends not just on current forcing but also on the history of the forcing. This topic is called delayed linear response, which is developed at length. Contour integration, when combined with Fourier transforms, provides the solution of various types of initial-value and boundary-value problems in infinite and semi infinite domains.

The aim of this chapter is to evaluate the potential role of Islamic finance as a tool for bridging the gap in current biodiversity financing in the MENA region. It examines the legal and institutional challenges to Islamic biodiversity financing in the MENA region and proffers recommendations on how to address them. This chapter examines the legal framework for advancing Islamic financing for biodiversity in the MENA region. It clarifies the role of Islamic financing approaches in addressing the resources gap, the legal barriers to its effective implementation across the MENA region, and recommendations on how to address such gaps.

Explores relationship of law to communal agriculture in three contexts; Indigenous communal grazing; Spanish and Mexican land grants; and Colorado state law of property rights.

This chapter presents themes that appear in earlier chapters and makes the case for legal reform to create an agricultural framework that represents the “real” west, rather than John Dutton’s west.

The rules of macroscopic elastic response are derived in an exact way by first stating the time rate at which mechanical work is performed in deforming a collection of molecules, which is the time rate at which internal elastic energy is being reversibly stored in the molecular bonds. From this work rate, the definition of the average stress tensor is obtained as well as the exact statement of the strain rate. An additional time derivative of the average stress tensor then gives Hooke’s law in its most general nonlinear form. How the elastic stiffnesses in Hooke’s law change with changing strain is derived. Displacement is defined and the shape change and volume change of a sample are understood through how the displacements of the surface bounding the sample are related to the strain tensor. Elastodynamic plane body-wave response is obtained, as is reflection and refraction of plane body waves from an interface and evanescent surface waves. It is shown how sources of elastodynamic waves such as cracking and explosions are represented as equivalent body forces.