Efficient and thorough data collection and its timely analysis are critical for disaster response and recovery in order to save peoples lives during disasters. However, access to comprehensive data in disaster areas and their quick analysis to transform the data to actionable knowledge are challenging. With the popularity and pervasiveness of mobile devices, crowdsourcing data collection and analysis has emerged as an effective and scalable solution. This paper addresses the problem of crowdsourcing mobile videos for disasters by identifying two unique challenges of 1) prioritizing visual-data collection and transmission under bandwidth scarcity caused by damaged communication networks and 2) analyzing the acquired data in a timely manner. We introduce a new crowdsourcing framework for acquiring and analyzing the mobile videos utilizing fine granularity spatial metadata of videos for a rapidly changing disaster situation. We also develop an analytical model to quantify the visual awareness of a video based on its metadata and propose the visual awareness maximization problem for acquiring the most relevant data under bandwidth constraints. The collected videos are evenly distributed to off-site analysts to collectively minimize crowdsourcing efforts for analysis. Our simulation results demonstrate the effectiveness and feasibility of the proposed framework.